ANALYSIS OF CARANGIFORM UNDULATION BASED ON VIRTUAL POWER PRINCIPLE

Most fish in nature achieve propulsion through undulatory movements, which are the result of the interaction between the deforming fish body and the surrounding fluid. To study the response of the fluid can enhance our understanding of undulatory propulsion and flow control. A two-dimensional deforming airfoil is used to model the carangiform fish. The flow field generated by fish body and the fluid forces acting on the fish body were obtained by using computational fluid dynamics. Using the principle of virtual power, the thrust on the fish body was decomposed into four parts, which are the instantaneous contribution of the boundary acceleration, the contribution of the relative magnitude of fluid rotation and strain rate in the flow field, the wall friction-like component and the wall friction component. The results show that the instantaneous contribution of the boundary acceleration is the main source of positive thrust. The 80% of the thrust contribution of this term comes from the instantaneous boundary acceleration movement of the rear 20% of the fish body. The fluid rotation and strain rate in the boundary layer on both sides of the fish tail and the friction contribute to resistance. For high Reynolds number, the negative contribution of the relative magnitude of fluid rotation and strain rate is stronger than that of wall friction, while for low Reynolds number, it is lower than that of wall friction. However, the wall friction-like component is always smaller compared to the other three terms. In the analysis of the scaling law of undulatory propulsion, it was found that there is a component independent of the Reynolds number which is provided by the first two parts, while the other component that is dependent on the Reynolds number is provided by the last three parts. Furthermore, the frictional force and the friction-like force provide constant resistance.