A vibration excitation system has been developed to excite the rotor blades of an axial compressor, in the specified nodal diameter mode and at the specified frequency, by injecting additional compressed air into the compressor flow path. The system was fitted to the Rofanco compressor test bench at the University of Stellenbosch in South Africa. A two-way staggered fluid-structure interaction (FSI) model was constructed that was capable of simulating the vibrations of the rotor blades excited by the vibration excitation system. The results of the FSI simulations were verified using available experimental data. It was concluded that the FSI model is able to recreate the vibrations of the rotor blades with sufficient accuracy. The results of the FSI simulations also indicated that the vibration excitation system should be capable of exciting the blades in the selected mode shape and at the selected frequency, provided the excitation frequency is close to the natural frequency of the first bending mode of each rotor blade.

Purpose When simulating fluid-structure interaction (FSI), it is often essential that the no-slip condition is accurately enforced at the wetted boundary of the structure. This paper aims to evaluate the relative strengths and limitations of the penalty and Lagrange multiplier methods, within the context of modelling FSI, through a comparative analysis. Design/methodology/approach In the immersed boundary method, the no-slip condition is typically imposed by augmenting the governing equations of the fluid with an artificial body force. The relative accuracy and computational time of the penalty and Lagrange multiplier formulations of this body force are evaluated by using each to solve three test problems, namely, flow through a channel, the harmonic motion of a cylinder through a stationary fluid and the vortex-induced vibration (VIV) of a cylinder. Findings The Lagrange multiplier formulation provided an accurate solution, especially when enforcing the no-slip condition, and was robust as it did not require “tuning” of problem specific parameters. However, these benefits came at a higher computational cost relative to the penalty formulation. The penalty formulation achieved similar levels of accuracy to the Lagrange multiplier formulation, but only if the appropriate penalty factor was selected, which was difficult to determine a priori. Originality/value Both the Lagrange multiplier and penalty formulations of the immersed boundary method are prominent in the literature. A systematic quantitative comparison of these two methods is presented within the same computational environment. A novel application of the Lagrange multiplier method to the modelling of VIV is also provided.