# Best Practice Advice AC6-15

# Vortex ropes in draft tube of a laboratory Kaplan hydro turbine at low load

## Application Area 6: Turbomachinery Internal Flow

### Application Challenge AC6-15

# Best Practice Advice

## Key Fluid Physics

The runner rotation leads to fluctuations due to the interaction of runner blades with guide vanes (rotor–stator interaction). An imbalance of the runner or an asymmetry of the stator also leads to pulsations. These pulsations propagate to the spiral case and can interfere with each other. Rotor–stator interaction is determined by a combination of the numbers of guide vanes and runner blades. Different modes are excited depending on their ratio. The intensity of these pulsations is strongly influenced by the radial clearance between the guide vanes and the runner. The frequency of these pulsations is usually high and it is of the order of several tens of the runner rotation frequency. Karman vortices can be formed on the vanes of the stator, guide vanes or runner blades. Fluctuations associated with Karman vortices can resonate with the vane body. If the body is sufficiently flexible, its vibrations may have the opposite effect on the vortex sheet. The profile of the vane trailing edge has a significant impact on the intensity of these pulsations. Thus, this requires a high precision when manufacturing the trailing edge. The fluctuations associated with the Karman vortices have an even higher frequency, exceeding the runner rotation frequency by a factor of 100 or even more. However, the greatest problems are caused by low-frequency pulsations in the draft tube. There are different vibration – generating mechanisms, some of them are associated with the precession of the vortex core (PVC). Precession of the vortex core occurs under partial load (at a discharge rate of 0.5–0.85 of the optimal value), where the flow has a considerable residual swirl. Vortex breakdown in such a flow leads to the formation of a recirculation zone at the flow axis and the rotation of the corkscrew vortex rope around it. The precession of the vortex rope is a serious danger for the hydraulic turbine equipment. Intense flow-induced pulsations lead to strong vibrations of the hydraulic turbine structure that can lead to damage in case of resonance. Pressure pulsations, generated by a precessing vortex rope, may also affect cavitation processes, enhancing cavitation erosion. Cavitation may enhance all the other pulsations.

## Application Uncertainties

The complexity of the geometry, curved and bladed regions, tip-clearance and rotor-stator interaction, oscillation of the runner rotational speed which is absent in numerical simulations are some sources of uncertainties which make a high fidelity CFD model difficult to assemble.

## Computational Domain and Boundary Conditions

The computational domain included all the elements constituting the turbine system: guide vane, runner and draft tube. At the input, a fixed flow rate was obtained from the experiment. At the output, a fixed pressure was set. This approach was found to produce realistic results.

A specific issue in the computer simulation of hydraulic turbines is the treatment of the rotating runner and the rotor-stator interaction. As discussed above, several approaches can be found in the literature, i.e. dynamic, sliding and moving grid methods and those based on a moving reference frame. In the present work paper, the modelling of the runner rotation was performed in the rotated reference frame for the runner zone. The obtained results are then rotated with the runner rotation speed and as such imposed as the inflow field for the inlet into the draft tube. Earlier test calculations proved that this approach is credible for describing the integral flow characteristics including the dominant flow pulsations. A comparison with the computationally more demanding method using sliding meshes showed that for this type of flows with a focus on draft tube dynamics the results are almost the same.

## Discretisation and Grid Resolution

The convective terms should be discretised by second-order schemes, and the CFL number should be kept below 1.0. Grid issues have been discussed above. It is clear that the 2M grid is too coarse for an LES, but interestingly, the LES on a 6M grid produced the main flow features - the pressure pulsations, velocity profiles and the *rms* of their fluctuations in good agreement with results for 19.3M cells. This relative insensitivity of LES to the grid refinement above 6M is attributed partially to a carefully designed mesh in the shear layers to meet the resolution criterion based on the “shear” scale (see below), but also to the fact that the flow is dominated by large-scale helical vortex structures, unaffected by the small-scale stochastic turbulence that may have remained unresolved on the 6M grid.

## Physical Modelling

The computations have shown that the two linear eddy viscosity models on the 2M grid could not maintain the unsteadiness and failed to reproduce the essential flow features, but on a finer grid of 6 M resulted in unsteady solutions with improved mean-flow patterns, though still failing to capture the precessing twin-helix structures and the pressure pulsations. In contrast, the second-moment closure (Re-stress) model on the same 2M mesh recovers well both the mean velocity field, the *rms* of its fluctuations, as well as the specific helical double rope structure in accord with experiments and LES. Similar performance is returned by DES.

The origin of the LEVM underperformance is traced to a too high eddy viscosity as a consequence of an excessive (unconditionally positive) production of the turbulent kinetic energy due to the models' inability to account for the turbulent stress anisotropy and the stress-strain phase lag, both naturally accounted for by the RSM. This leads to a much larger modelled kinetic energy and the effective viscosity compared to the RSM. In flows with a weak internal forcing or using a too coarse grid, LEVM can fail to capture flow unsteadiness. If it does, the resolved motion is weak and manifests in a smaller resolved kinetic energy, which diminishes the models' sensitivity and receptivity to internal flow instabilities compared to RSM (and, of course, to DES where the bulk flow is resolved by LES).

It was also shown that the LES on two very different grids, with 6M and 19.3M cells, returned very similar results. This, to some extent surprising finding, is attributed to the fact that the cell size was optimized to be smaller than the Corrsin shear scale, while resolving the fine stochastic scales proved not to be essential for the flow dominated by strong large-scale coherent vortical structures.

## Recommendations for Future Work

The focus of future works should be put on the control of the loss-sources in the draft tube, such as decreasing the pressure pulsations, shrinking the size of the vortex rope and the on-axis recirculation region, and even the prevention of the vortex breakdown. The different control techniques should be investigated to decrease the harmful effects of the vortex breakdown and pressure pulsations. The detailed simulations should be extended to a variety of geometries used in hydropower. Flows under different operating conditions and with different geometrical details should be studied.

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Contributed by: **A. Minakov [1,2], D. Platonov [1,2], I. Litvinov [1], S. Shtork [1], K. Hanjalić [3]** —

[1] Institute of Thermophysics SB RAS, Novosibirsk, Russia,

*[2] Siberian Federal University, Krasnoyarsk, Russia*,

*[3] Delft University of Technology, Chem. Eng. Dept., Holland*.

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