New Simulation Strategy for an Oscillating Cascade in Turbomachinery Using Immersed-Boundary Method

Abstract

Based on the immersed-boundary method, a numerical simulation for an oscillating cascade is established and the relevant analysis is presented with emphasis on the physical understanding of fluid-structure interaction. To validate the method, two simulation cases, an oscillating circular cylinder at a low Keulegan-Carpenter number and a flapping airfoil, are performed and the results are in good agreement with the previous research. In the oscillating cascade simulation, it is found that the reduced velocity U is a very sensitive factor which affects the critical stable boundary in the present examples. On the other hand, the effects of interblade phase angles on the system stability are also discussed. In particular, it is worth noting that the same process is applied to several test cases without generating any body-fitting grid. Therefore, the method shows a significant time savings in the computational process for such a complicated fluid-structure interaction problem.damping ratio in transverse direction c = structural damping ratio in rotational direction D = diameter of the cylinder Fx; t = external force F h = lift in transverse direction F = moment around the airfoil elastic center f = oscillating frequency fx s ; t = force per unit area applied by the body to the fluid f n = natural frequency of the oscillating blade h = transverse movement displacement _ h = transverse movement velocity h = transverse movement acceleration h x = mesh size in x direction h y = mesh size in y direction I = inertial moment around the airfoil elastic center KC = Keulegan-Carpenter number k h = structural stiffness ratio in transverse direction k = structural stiffness ratio in rotational direction l = reference length m = mass of the airfoil m = nondimensional mass of the body px; t = flow pressure Re = Reynolds number r = length between surface point and elastic center S = static moment around the airfoil elastic center T = overall period of the system Ux; t = flow velocity Ux s ; t = flow velocity on the body surface U max = maximum velocity of the cylinder motion U 1 = uniform flow velocity U = reduced velocity vx s ; t = body surface velocity x = computational mesh coordinates x s = body surface coordinates x = Cartesian components of x xt = translation motion position x 0 t = translation motion velocity y = Cartesian components of x = feedback function negative constants 0= rotational initial angle = feedback function negative constants 0 = rotational amplitude = airfoil surface = two-dimensional delta function = structural damping ratio = rotational angle _ = rotational angular velocity = rotational angular acceleration 1 = density of fluid = difference phase between xt and t r = function to construct

Suppression of vortex-induced vibration using the rotary oscillation of a cylinder

“…The method shows the importance of time saving in the computational process for the fluid-structure interaction problem because the governing equations are discretized on a fixed orthogonal mesh, even if the boundaries move arbitrarily in the computational domain. In Zhong and Sun's study, 21 an oscillating cascade was simulated by using the immersed boundary method, especially, some complicated non-linear coupling phenomena were captured. The present method has been used to study the modes of vortex formation and transition to three-dimensionality in the wake of a freely vibrating cylinder by Du et al 22 In this study, the VIV of a rotationally oscillating cylinder is numerically studied with zero structural damping coefficient to obtain maximum response.…”

Generation of Vortex Lift Through Reduction of Rotor/Stator Gap in Turbomachinery

“…To avoid data exchange at the interface between blade rows, a numerical scheme is established to simulate the unsteady flow associated with the rotor/ stator interaction. The present method has been employed for treating fluid-structure interactions by Zhong and Sun [40], Du et al [41], and Du and Sun [42]. Several complicated nonlinear coupling and flow transition phenomena were captured.…”

Vortex-Lift Mechanism in Axial Turbomachinery with Periodically Pitched Stators

“…Only a single zone is needed, and the difficulties of generating multiple grids and treating interfacial boundaries are eliminated. The present method has been used in previous work by Zhong and Sun [42] and by Du et al [43,44] to study fluid-structure interactions, capturing complicated nonlinear coupling and flow transition phenomena. The same authors have used this method to simulate the unsteady flow of a modulation fan with pitching blades [45], which can generate low-frequency sound at high sound pressure levels.…”