Sergey G. Skripkin

The precessing vortex core (PVC) in the draft tube of a Francis turbine at part load produces severe pressure pulsations that threaten structural integrity. Efficient active control of PVC demands an understanding of how momentum injection alters the spatial topology and coherent energy of this global instability. This experimental study, conducted on a canonical expanding swirling flow with ten actuators delivering axial, radial, and combined jets, employs synchronized planar PIV and wall-pressure measurements to capture the velocity and pressure fields. Robust correlations are obtained: on-axis and vortex core tangential velocity fluctuations are linearly coupled, circulation scales linearly with precession radius, and helical pitch increases as the precession orbit contracts. Notably, the wall-pressure amplitude depends quadratically on the PVC’s turbulent kinetic energy contribution, showing that spatial contraction enhances the attenuation. These interlinked scaling laws provide a physics-based framework connecting control input to vortex reconfiguration and dynamic load, guiding low-energy control design for hydraulic turbines and other swirling flow devices.

This study investigates the active control of the precessing vortex core, a detrimental global instability in strongly swirling flows. Experiments were conducted on a canonical aerodynamic model, employing time-resolved particle image velocimetry, laser Doppler anemometry, and acoustic measurements to characterize the flow response. Ten distinct actuators, varying in orientation (axial, radial, and combined) and geometry, were used to inject control momentum, with the effort quantified by the dimensionless momentum flux coefficient Cμ. The results demonstrate that Cμ provides a linear scaling for the change of the integral swirl number. The change in the global flow field is analyzed using the strain-rate tensor and the spatial distribution of tangential velocity pulsations. Targeted radial injection most effectively reduces angular momentum near the axis and interrupts the energy supply to the instability. A quadratic relationship is established, showing that the wall-pressure pulsations scale with the square of the amplitude tangential velocity fluctuations. The results provide physics-based guidelines for designing efficient, low-energy flow control systems to mitigate vortex-induced instabilities.

The precessing vortex core (PVC) is a fundamental global instability that dictates the dominant unsteady dynamics and energy transfer processes in swirling flows. This study presents a comprehensive experimental investigation of the spatial transformation of the PVC in an expanding swirling flow subjected to multi-jet injection. Using time-resolved particle image velocimetry synchronized with pressure measurements, we systematically quantify changes in key vortex parameters: precession radius, core diameter, helical pitch, and circulation with varying injection angles (axial, radial, and combined). The results demonstrate a profound spatial reorganization: a systematic contraction of the precession radius, a significant axial stretching reflected in an increased helical pitch, and a monotonic reduction in vortex circulation. These spatial modifications are successfully consolidated using the momentum flux coefficient, revealing clear scaling laws. This work establishes a direct causal link between the controlled manipulation of the PVC's spatial topology and the attenuation of its dynamic effects, providing a foundational insight for developing efficient control strategies in vortex-dominated flows.

The precessing vortex core (PVC) is a major source of low-frequency harmful pressure pulsations that constrain the stable operating range of Francis turbines under part-load regimes. This study presents an experimental demonstration of active frequency control for the PVC in an aerodynamic turbine model (at Reynolds number 1.5 × 10⁴), employing a resonant forcing strategy grounded in linear stability theory. Low-energy air injection with a momentum flux coefficient in the range of approximately 0.06% to 1.56% was applied via rotating actuators positioned within the flow region of highest receptivity. The core finding is the observation of frequency, where the PVC’s natural precession frequency synchronizes with that of the rotating actuator. A comparative analysis of actuator geometry revealed that a single-jet configuration achieves a significantly greater frequency shift, up to 22%, and a wider lock-in range than a dual-jet actuator (8% shift). This enhanced performance is attributed to the higher momentum flux density and more spatially coherent forcing generated by the single jet, which couples more effectively with the global instability mode. The results validate the successful adaptation of a highly efficient, physics-based control paradigm from reacting flows to hydraulic machinery, offering a promising approach to mitigate vortex-induced vibrations and expanding turbine operational flexibility.

This work aims to advance methods for the active control of vortex phenomena in hydraulic turbines. The investigation was conducted on a Francis turbine model operating under partial load conditions, where large-scale vortex structures develop, inducing high levels of pressure pulsations detrimental to turbine structural integrity. Control of the vortex core characteristics is based on the injection of supplementary jets through the central streamline body of the runner. Experimental results are presented for velocity fields under various flow control strategies, differing in the spatial orientation of the jets and their total flow rate. An analysis is presented of the integral flow characteristics and the evolving vortex structures downstream of the Francis turbine model runner. The mechanisms governing vortex core control under different supplementary jet injection methods are described. It is found that, irrespective of jet direction, a total injected flow rate of 3% of the main flow significantly suppresses pressure pulsations. However, radial jet injection (parallel to the runner plane) proves more effective than axial injection or a combination of both directions. Alongside the injected flow fraction, the dimensionless momentum flux coefficient is identified as a key parameter governing the effectiveness of control on the precession vortex core.

Our experiments revealed an interesting nonlinear physics phenomenon: a triple hysteresis and a few bifurcations in a compact two-liquid vortex flow driven by the bottom disk rotation. Two immiscible liquids fill a vertical cylindrical container. The slow rotation drives toroidal axisymmetric steady circulations of both liquids. The lower liquid moves up near the sidewall and down near the axis, eventually forming a funnel filled with the upper liquid. If the angular velocity ωd of the disk exceeds the first critical value ω1, then the flow pattern loses axial symmetry and, in particular, the funnel in the horizontal cross section from circular becomes ellipsoidal. If ωd exceeds the second critical value ω2, then the flow becomes oscillatory in time. If ωd exceeds the third critical value ω3, then the elliptical funnel splits into two funnels whose axes differ from the axis of the cylinder. If we now start eventually reducing ωd, then the flow in the reversed order passes qualitatively the same states, but with smaller critical values of ωd. These three different critical values of ωd indicate a triple hysteresis. A hysteresis—the dependence of flow state on the prehistory—is a typical feature of compact two-fluid rotating flows. However, the triple hysteresis discovered here is a new striking flow phenomenon.

It has been found, for the first time, that rotating polygons (m = 1, 2) can exist in a system of two immiscible fluids, which can be in three different steady states: stable funnel, cycling switching, and rotating twin funnel. These states are achieved due to different disk acceleration values at fixed aspect ratio (h/R) = 1 and Reynolds numbers. The acceleration time of rotating disk is found to have a significant effect on instability development.