Combined surging and pitching of an airfoil at the identical frequency (i.e. synchronously), at four different phase differences, was investigated theoretically and experimentally. The most general unsteady theoretical formulation was adopted to calculate the lift coefficient, and then extended to explicitly compute the unsteady bound vortex sheet. This was used for comparison with experiments and facilitated the computation of both Joukowsky and impulsive-pressure lift contributions. Experiments were performed using a symmetric 18 % thick airfoil in an unsteady wind tunnel at an average Reynolds number of $3.0\times 10^5$, with a free-stream oscillation amplitude of 51 %, an angle-of-attack range of $2^\circ \pm 2^\circ$ and a reduced frequency of 0.097. In general, excellent correspondence was observed between theory and experiment, representing the first direct experimental validation of the general theory. It was shown, both theoretically and experimentally, that the lift coefficient was not accurately represented by independent superposition of surging and pitching effects, due to variations in the instantaneous effective reduced frequency not accounted for during pure pitching. Deviations from theory, observed at angle-of-attack phase leads of $90^\circ$ and $180^\circ$, were attributed to bursting of separation bubbles during the early stages of the acceleration phase. The largest deviations occurred when the impulsive-pressure lift contribution was small relative to the Joukowsky contribution, because the latter was most affected by bubble bursting. Bubble bursting resulted in large form-drag oscillations that occurred at identical phase angles within the oscillation cycle, irrespective of the phase difference between surging and pitching, as well as in the absence of pitching.

The lobe dynamics andmass transport between separation bubble and main flow in flow over airfoil are studied in detail, using Lagrangian coherent structures (LCSs), in order to understand the nature of evolution of the separation bubble. For this problem, the transient flow over NACA0012 airfoil with low Reynolds number is simulated numerically by characteristic based split (CBS) scheme, in combination with dual time stepping. Then, LCSs and lobe dynamics are introduced and developed to investigate themass transport between separation bubble and main flow, from viewpoint of nonlinear dynamics. The results show that stable manifolds and unstable manifolds could be tangled with each other as time evolution, and the lobes are formed periodically to induce mass transport between main flow and separation bubble, with dynamic behaviors. Moreover, the evolution of the separation bubble depends essentially on the mass transport which is induced by lobes, ensuing energy and momentum transfers. As the results, it can be drawn that the dynamics of flow separation could be studied using LCSs and lobe dynamics, and could be controlled feasibly if an appropriate control is applied to the upstream boundary layer with high momentum.

A three-dimensional Navior-Stokes analyzer based on control volume method is developed to simulate the complex flow field within a turbomachinery. With VKI-CT2 turbine blade as the test model, numerical results are compared with experimented data and shows the existence of separation-transition bubble and the interaction of shock with turbulent boundary layer flow. The governing Navier-Stokes equations are solved by an improved numerical method that uses an upwind flux-difference split scheme for spatial descretization and an explicit optimally smoothing multi-stage scheme for time integration. Turbulent stresses are approximated by modifying Baldwin-Lomax algebraic, k-ε, R-k-ε and RNG k-ε turbulence models. According to the results of this research, this analyzer can indeed effectively modulate and simulate the aerodynamic characteristic of the transonic turbine rotor near the endwall.