The 2D lumped wake vortex method applied to unsteady flapping

PurposeAdvancements in aerospace technologies, which rely on unsteady fluid dynamics, are being hindered by a lack of easy to use, computationally efficient unsteady computational fluid dynamics (CFD) software. Existing CFD platforms are capable of handling unsteady flapping, but the time, money and expertise required to run even a basic flapping simulation make design iteration and optimization prohibitively expensive for the average researcher.Design/methodology/approachIn the present paper, a remedy to model the effects of viscosity is introduced to the original vortex method, in which the pitching moment amplitude grew over time for simulations involving multiple flapping cycles. The new approach described herein lumps far-field wake vortices to mimic the vortex decay, which is shown to improve the accuracy of the solution while keeping the pitching moment amplitude under control, especially for simulations involving many flapping cycles.FindingsIn addition to improving the accuracy of the solution, the new method greatly reduces the computation time for simulations involving many flapping cycles. The solution of the original vortex method and the new method are compared to published Navier–Stokes solver data and show very good agreement.Originality/valueBy utilizing a novel unsteady vortex method, which has been designed specifically to handle the highly unsteady flapping wing problems, it has been shown that the time to compute a solution is reduced by several orders of magnitude (Denda et al., 2016). Despite the success of the vortex method, especially for a small number of flapping cycles, the solution deteriorates as the number of flapping cycles increases due to the inherent lack of viscosity in the vortex method.

Reduced-order unsteady aerodynamic models at low Reynolds numbers

In this paper we develop reduced-order models for the unsteady lift on a pitching and plunging aerofoil over a range of angles of attack. In particular, we analyse the pitching and plunging dynamics for two cases: a two-dimensional flat plate at $\mathit{Re}= 100$ using high-fidelity direct numerical simulations and a three-dimensional NACA 0006 aerofoil at $\mathit{Re}= 65\hspace{0.167em} 000$ using wind-tunnel measurements. Models are obtained at various angles of attack and they are verified against measurements using frequency response plots and large-amplitude manoeuvres. These models provide a low-dimensional balanced representation of the relevant unsteady fluid dynamics. In simulations, flow structures are visualized using finite-time Lyapunov exponents. A number of phenomenological trends are observed, both in the data and in the models. As the base angle of attack increases, the boundary layer begins to separate, resulting in a decreased quasi-steady lift coefficient slope and a delayed relaxation to steady state at low frequencies. This extends the low-frequency range of motions that excite unsteady effects, meaning that the quasi-steady approximation is not valid until lower frequencies than are predicted by Theodorsen’s classical inviscid model. In addition, at small angles of attack, the lift coefficient rises to the steady-state value after a step in angle, while at larger angles of attack, the lift coefficient relaxes down to the steady-state after an initially high lift state. Flow visualization indicates that this coincides with the formation and convection of vortices at the leading edge and trailing edge. As the angle of attack approaches the critical angle for vortex shedding, the poles and zeros of the model approach the imaginary axis in the complex plane, and some zeros cross into the right half plane. This has significant implications for active flow control, which are discussed. These trends are observed in both simulations and wind-tunnel data.

Analysis of Fluid-Structure Interaction in a Steam Turbine Throttle Valve

Throttle valves in steam turbines often operate at very small lift positions during turbine startup. The large pressure differentials across these valves, combined with the very small openings at the valve seat, result in large pressure drops across these valves and high local steam Mach numbers. A steam turbine throttle valve operated under these conditions was found to be undergoing self-excited vibration. Stress and structural dynamic finite element analyses (FEA) were performed to identify the structural mode for the valve oscillations. A three-dimensional transient computational fluid dynamics (CFD) analysis of the valve revealed an unsteady fluid dynamics phenomenon in the pressure balancing arrangement that served as a forcing function for this vibration. Valve modifications were implemented as a result of these analyses. The improved valve has performed successfully, and the design modifications have been incorporated in other production valves.

The Unsteady Fluid Dynamics of a Pair of Pitching Airfoils Using Computational Fluid Dynamics

The objective of the present study is to investigate the low Reynolds number (LRN) fluid dynamics of two airfoils in pitching oscillations. The airfoils are in a tandem configuration and perform in-phase oscillations. Navier-Stokes (NS) equations with Finite Volume Method (FVM) are used and the instantaneous aerodynamic force coefficients are analyzed. The effect of amplitude of pitching oscillations and Re are investigated on the fluid forces. It is found that the amplitude of pitching oscillations is of primary importance to the fluid forces, affecting them quantitatively and qualitatively. Re is found to be of secondary importance compared to the effects of the amplitude of pitching oscillations. It mainly affects the magnitude of the forces.