Study On The Flow-induced Bending-torsional Coupling Vibration Characteristics Of A Near-wall Flexible Hydrofoil

Hydrofoils are widely used in the fields of fluid machinery and marine ship engineering,such as blades of pumps and turbines,flap rudders and fin stabilizers of ships,shell rudders,bow and stern rudders and propellers of submarines,etc.Hydrofoil can not only provide lift and thrust,but also improve the stability and maneuverability of ships and submarines.Hydrofoils are often made of copper alloys.With the development of material science,it has been found that hydrofoils made of composite materials（flexible hydrofoils）have advantages in hydrodynamic propulsion,cavitation effect,noise compared with traditional rigid hydrofoils.However,the deformation of the flexible hydrofoil has a greater impact on its performance.In practical engineering,hydrofoils are often affected by nearby solid walls,such as the casing of pumps and turbines,and the seabed where autonomous underwater vehicles work.The influence of the wall on the flexible hydrofoil cannot be ignored.Therefore,this paper studied the flow-induced bending-twisting vibration of the flexible hydrofoil near the wall,and analyzes the effects of the wing-wall distance（H）and the initial angle of attack（α₀）on the bending-twisting vibration with different reduced velocities.Firstly,this paper studied the flow characteristics around the rigid hydrofoil near the wall,discussed the influence of wing-wall distance and initial angle of attack on its hydrodynamic performance and wake structure,and compared it with the flow characteristics of isolated rigid hydrofoil.The study found that the lower the wing-wall distance,the higher the lift-drag ratio of the rigid hydrofoil.When H=0.3C,the maximum lift-drag ratio reached 2.96,which is 30%higher than that of the isolated rigid hydrofoil.When the initial angle of attack is 15°and 10°,the lift-drag ratio of the rigid hydrofoil fluctuates greatly,while the lift-drag ratio is stable when the initial angle of attack is 25°and 5°.When the initial angle of attack increases,the lift-drag ratio decreases,but the lift coefficient and drag coefficient increase accordingly.Whenα₀=5°,the lift-drag ratio is up to 3.9,which is 1.15 times higher thanα₀=25°.The transformation of the vortex has a great influence on the lift coefficient and drag coefficient of the hydrofoil.When the vortex mode is"2S",the standard deviation of the lift coefficient,the time-average lift-drag coefficient and the lift-drag ratio of the hydrofoil will increase;When the vortex mode is"U"type,the standard deviation of the lift coefficient and the time-averaged lift-drag coefficient of the hydrofoil are lower;when the wake vortex mode is"2S^*"type,the hydrofoil wake is in the transition state from“2S”to“U”.There is a sudden drop in the standard deviation of the lift coefficient,the time-averaged lift-drag coefficient and the lift-drag ratio with the rises of U^*.Then,the flow-induced bending-twisting vibration of the flexible hydrofoil at different wing-wall distances is studied,and the effects of the wing-wall distance on the bending-twisting vibration,frequency response,hydrodynamics and wake structure of the flexible hydrofoil are discussed.It is found that when 3≤U^*≤6,the bending-twisting vibration is very weak,the standard deviation of the lift coefficient is similar to that of the rigid hydrofoil,but the value is smaller,and the lift-drag coefficient is close to that of the rigid hydrofoil;When 8≤U^*≤12,the time-averaged lift-drag coefficient and lift-drag ratio of flexible hydrofoils are higher than those of rigid hydrofoils due to the frequency"lock-in"phenomenon of bending vibration and twisting vibration.Finally,the flow-induced bending-twisting vibration of the flexible hydrofoil near the wall under different initial angles of attack is studied,and the effects of the initial angles of attack on the bending-twisting vibration,frequency response,hydrodynamics and wake structure of the flexible hydrofoil are discussed.The study found that whenα₀=5°,there is no bending vibration and twisting vibration of the flexible hydrofoil;Atα₀=10°andα₀=15°,when the frequency"lock-in"phenomenon occurs,the bending and twisting vibration became strong.Atα₀=20°andα₀=25°,with the increase of the reduced velocity,the bending amplitude first gradually decreases and then tends to be stable,while the twisting amplitude basically shows an upward trend.The larger the initial angle of attack of the flexible hydrofoil,the larger the bending amplitude and the twisting amplitude.Compared with rigid hydrofoils,the standard deviation of the lift coefficient of flexible hydrofoils decreases greatly,but the lift-drag ratio changes very little.However,when the frequency is locked,the standard deviation of the lift coefficient and the time-average lift-drag ratio increase.