The vortex-based propulsive systems’ enhanced performance greatly contributes to the vortex added-mass effect, which was initially developed to explain the added drag when a solid body accelerates in fluids. However, the solution of the instantaneous vortex added-mass coefficient is still remaining a question because vortices always do not have a stable geometric shape like solid bodies. In this paper, the formation of a canonical vortex ring is performed to investigate the nature of vortex added-mass and explore a solution for estimating the vortex added-mass coefficient. The vortex ring is generated by a piston-cylinder apparatus, and the time-dependent flow fields are recorded by particle image velocimetry technique. The ridges of finite-time Lyapunov exponent are applied to identify the Lagrangian boundary of the vortex ring. It is found that a part of the ambient fluids is entrained by the vortex ring when it propagates downstream, resulting in the growth of the vortex ring. Besides, a significant drift of the ambient fluid is observed to bypass the Lagrangian boundary of the vortex ring and reveals the nature of the vortex added-mass. Thus, the added-mass coefficient of the vortex is redefined as the ratio of the volume of the Lagrangian drift fluids in finite time interval step to the vortex volume at that instant. By referring to McPhaden’s method to estimate the added-mass of a solid body, a method based on the multiple material lines with relative-timestep is developed to estimate the volume of Lagrangian drift fluids induced by the vortex added-mass. Then, an empirical criterion for determining the material line number and the finite time interval step is suggested for the vortex ring flow, and the eventual vortex added-mass coefficient calculated by the volume of Lagrangian drift fluids is found to well agree with the results of Brennen. Moreover, the method based on multiple material lines for calculating Lagrangian drift fluids’ volume suggests a potential solution for estimating the added-mass coefficient of arbitrary vortex structures.

基于涡流的推进系统的增强性能极大地促进了涡流附加质量效应，该效应最初被开发用于解释固体在流体中加速时的附加阻力。然而，瞬时涡流附加质量系数的求解仍然是一个问题，因为涡流并不总是像固体那样具有稳定的几何形状。在本文中，通过典型涡环的形成来研究涡附加质量的性质并探索估计涡附加质量系数的解决方案。涡环由活塞-气缸装置产生，时变流场由粒子图像测速技术记录。应用有限时间李雅普诺夫指数的脊来识别涡环的拉格朗日边界。发现部分环境流体在向下游传播时被涡环夹带，导致涡环增大。此外，观察到周围流体的显着漂移绕过涡环的拉格朗日边界，揭示了涡流附加质量的性质。因此，涡流的附加质量系数被重新定义为有限时间间隔步长内拉格朗日漂移流体的体积与该时刻涡流体积的比值。参考McPhaden估计固体附加质量的方法，提出了一种基于多条相对时间步长的物质线的方法来估计涡流附加质量引起的拉格朗日漂移流体的体积。然后，提出了确定涡环流的材料线数和有限时间间隔步长的经验准则，发现由拉格朗日漂移流体的体积计算的最终涡流附加质量系数与Brennen的结果非常吻合。此外，用于计算拉格朗日漂移流体体积的基于多条材料线的方法为估计任意涡结构的附加质量系数提供了一种潜在的解决方案。