Book Description

"This thesis presents a thorough analysis of the unsteady two- and three-dimensional confined periodic flows with time-variable inflow velocity, and the unsteady viscous periodic flows past stationary airfoils at low Reynolds numbers. The research was performed in two case studies: (i) analysis of the two-dimensional and three-dimensional unsteady confined periodic flows; and (ii) analysis of the unsteady viscous periodic flows past stationary airfoils. The first part of this thesis presents a time spectral method to solve the unsteady confined periodic flows at low Reynolds numbers. This time spectral method considers truncated Fourier series expansions for the fluid variables and pressure, which reduces the solution of the unsteady incompressible Navier-Stokes equations to the solution of several steady harmonic flow component problems that are solved sequentially. The developed time spectral method is applied to the solution of the unsteady confined periodic flows in a two-dimensional and then in a three-dimensional backward-facing step channel with time-variable inflow velocity, which displays flow separation regions on the upper and lower walls. The method is successfully validated in comparison with the experimental results presented by Armaly et al. and by Lee and Mateescu, and with the numerical results obtained by the time-accurate methods. The obtained results are presented for various flow and geometric parameters, such as the Reynolds number, inflow velocity amplitude, reduced frequency of oscillation, and the aspect ratio of the channel cross-section.The analysis of unsteady viscous periodic flows past stationary airfoils at low Reynolds numbers using a developed time spectral method is the second part of this thesis, based on the Navier-Stokes equations for incompressible flows. This is completely justified because for Reynolds numbers smaller than 5000 and for airfoil chord length between 20 and 40 cm the Mach number is below 0.01. Obviously, for these low Reynolds numbers it is not justified to use the Navier-Stokes equations for compressible flows, as it was done by other authors for higher Reynolds numbers. In this case, the time spectral method, in which the nondimensional fluid velocity components and pressure are expressed by truncated Fourier series expansion, is applied to study the unsteady effects on the aerodynamic coefficients of the stationary airfoils generated by the unsteadiness of the flow separations occurring on the upper surface of the airfoil. Periodic variations of the aerodynamic coefficients of the lift and drag appear at incidences larger than six or eight degrees depending on the Reynolds number and airfoil shape. These time spectral method solutions are validated by comparison with previous numerical results obtained by the time-accurate method. The solutions are presented for the unsteady lift and drag coefficients for several symmetric and cambered NACA airfoils. The influence of various flow and geometric parameters, such as Reynolds number and airfoil relative thickness and camber, on the unsteady aerodynamic coefficients is also performed and presented in this part of the thesis.These time spectral methods provide the solution of such periodic flows with a significant reduction of the computational time in comparison with the time-accurate methods, which have to solve the transient flows that consume the majority of the time computations until the periodic flow solution is obtained.The time spectral methods developed in this thesis are completely original and the solutions are validated with experimental results and numerical solutions found in the literature. The effect of the lateral walls in the experimental confined configurations and the time variation of the aerodynamic lift and drag coefficients of the stationary airfoils due to the formation of the unsteady flow separations at low Reynolds numbers are especially analyzed"--