Scaling the dynamic response and stability of composite hydrodynamic lifting surfaces
G. W. Ng, A. S. Vishneek, J. R. R. A. Martins, and Y. L. Young
Composite Structures, 115148, 2022
Imperfectly scaled models are commonplace in aerodynamics and hydrodynamics because few facilities can meet all the flow and structural scaling requirements. The objectives of this work are to (1) derive and numerically validate scaling relations for the steady-state and dynamic hydroelastic response and stability of hydrodynamic composite lifting surfaces and (2) to investigate the effect of imperfect scaling on the steady-state and dynamic response, as well as hydroelastic stability of said surfaces. We derive proper scaling laws and validate them through numerical simulations using unsteady potential flow and composite beam theory. We investigate the prediction of inception of a new, low-frequency mode that only develops at sufficiently high speeds using scaled models. We demonstrate scaling effects on the modal frequencies, damping coefficients, and hydroelastic instability boundaries by comparing cases with fully enforced scaling laws and cases with relaxed similarities. Using the same material for both the prototype and reduced length-scale models results in imperfect scaling; the steady-state and dynamic hydroelastic responses are not scaled, and smaller length-scale models exhibit delayed hydroelastic instabilities. The conclusion is that using appropriate materials for model scale tests to satisfy Cauchy number similarity is necessary for similar steady-state response, but dynamic similarity additionally requires similar solid-to-fluid added mass ratio. Proper scaling allows one to accurately interpret and assess the performance and stability of full-scale flexible composite lifting surfaces such as foils, propulsors, turbines, fins, rudders, energy saving devices, and energy harvesters.