Numerical and experimental analyses were carried out to investigate the dynamic characteristics of liquid annular seals with helical grooves in the seal stator. In the numerical analysis, the governing equations were the momentum equations with turbulent coefficients and the continuity equation, all averaged across the film thickness and expressed using an oblique coordinate system in which the directions of coordinate axes coincided with the circumferential direction and the direction along the helical grooves. These governing equations were solved numerically to obtain the dynamic characteristics, such as the dynamic fluid-film forces, dynamic coefficients, and whirl-frequency ratio (WFR). The numerical analysis included the effect of both fluid inertia and energy loss at the steps between the helical groove and the land sections. In the experiments, the dynamic fluid-film pressure distributions, which were induced by a small whirling motion of the rotor about the seal center, were measured to obtain the dynamic characteristics. The equivalent numerical results reasonably agree with the experimental results, demonstrating the validity of the numerical analysis. The value of the tangential dynamic fluid force induced by the rotor whirling motion decreased with increasing the helix angle γ. Consequently, the values of the cross-coupled stiffness coefficient and WFR decreased with increasing γ and became negative for large γ. In general, pump rotors rotate with a forward whirling motion under normal operating conditions. Hence, the negative value of WFR for helically grooved seals contributes to rotor stability by suppressing the forward whirling motion of the rotor.

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