# Description

## Introduction

Computer simulations have been seen as a potential tool for capturing the subtleties of the development of instabilities and associated vortical and turbulence structures. Such information can be obtained by direct and large-eddy simulations (DNS, LES) over a range of important scales, but the accuracy of DNS and LES depends much on the numerical resolution. For complex configurations the Reynolds-averaged Navier-Stokes (RANS) approach, being computationally less demanding, has been considered as a more rational option for industrial purposes.

However, because of its empirical nature, the RANS approach in general has not been regarded as a trustful research tool, recognizing that its credibility depends much on the choice of the turbulence model to close the time- or ensemble-averaged conservation equations. Hybrid LES/RANS schemes (including detached eddy-simulations, DES), where LES is used in the flow bulk and a RANS model for the wall-adjacent, or complete wall-attached flow regions, are becoming popular and, by some in the community, are seen as the future industrial standard (Slotnick et al., 2014).

Using the here reported experimental data and a fine-grid LES as the reference, we analyzed the performance of two levels of RANS models representing the LEVM and RSM families, the basic DES and LES with WALE sub-grid scale viscosity in reproducing not only the time-averaged basic flow and turbulence properties in the turbine draft tube, but also the flow patterns, vortical structures and their relation with the, industrially most critical, frequencies and amplitudes of pressure pulsations, all in the range of off-design conditions. The material presented here is based on the work published in Minakov et al. (2017).

## Relevance to Industrial Sector

Common hydraulic turbomachinery has long reached a mature stage of development, and at design conditions usually performs with high efficiency and reliability. However, the ever-increasing share of intermittent and unpredictable wind and solar power in electricity generation requires higher flexibility of operation and fast load adjustment of the base power plants (including hydro) over a wide range of operating conditions. At part loads and in transient regimes the stability of the hydropower system can seriously be impaired leading to a decrease in efficiency, mechanical damage, fatigue and system failure. The intrinsic unsteadiness at suboptimal conditions leads often to vortex breakdown and precessing helical vortices in form of a single or twin rope behind the runner, which cause intense flow pulsations and vibrations of the turbine structure that pose a serious threat to the system reliability and safety. These issues have long been in the focus of experimental research complemented by some simplified analytics, but a full account of the three-dimensional time dynamics has remained to a large extent beyond the reach of even the most advanced laser-based measurements and diagnostics techniques.

## Design or Assessment Parameters

The design and assessment parameters for the test case considered here can be grouped into two categories, one characterizing the experimental facility and its operation, and the other being relevant for assessing the numerical modeling.

The first group includes the Reynolds number, ${\displaystyle {Re=U_{av}D/\mu }}$, the geometric parameters of the facility (the runner diameter D, geometry of the guide vane and runner blades, geometry of the draft tube), rotating speed of the runner, volume flowrate through the unit, specific speed the runner ${\displaystyle {n_{s}=nP^{1/2}/H^{5/4}}}$ and the swirl parameter ${\displaystyle {S=W_{max}/U_{max}}}$ = 0.78

The second group includes parameters that allow evaluating the reliability of the calculated data. In the present case, it is the vertical velocity component field in the central section, the vortex structure behind the impeller, the velocity components and their pulsations in different sections behind the impeller, pressure pulsations and their spectra in the diffuser of the draft tube.

## Flow Configuration

The flow configuration considered (see Fig. 1) is a 60:1 scaled-down laboratory model mimicking the draft tube of a Kaplan turbine, operating at a low load. The laboratory turbine actually does not look precisely like the typical Kaplan turbine, but nevertheless it was designed to generate the same flow conditions and featuring similar flow pattern in the draft tube as in a full-scale double regulated axial turbine. Namely, as demonstrated in Bosioc et al. (2009), Chen et al. (2010), Susan-Resiga (2008), the conditions in a real turbine set-up could be achieved in an experiment without having to replicate precisely the full geometry of the complete real turbine system (spiral chamber, stay vanes and guide vanes, rotor). What matters for studying the draft tube flow dynamics is the inflow velocity and turbulence field distribution after a real turbine entering the draft tube. These have been created using a set of two rows of blades (Fig. 1), designed to generate the draft tube inlet conditions that correspond to a real Kaplan turbine (Kuibin, Litvinov, Sonin, Ustimenko, & Shtork, 2016). To this effect one of the rows was set still, functioning as a guide vane of the turbine (with a uniform fluid inflow at a volumetric flowrate ${\displaystyle {\mathcal {Q}}}$). The second row forcedly rotates with frequency ${\displaystyle {f}}$ and is an analogue to the turbine runner. Thus, by controlling the two parameters ${\displaystyle {\mathcal {Q}}}$ and ${\displaystyle {f}}$ it is possible to experimentally simulate the modes of the turbine load.

 (a) (b) Figure 1: A photo of the experimental setup (a), and a sketch of the test section (b)

## Flow Physics and Fluid Dynamics Data

The considered volumetric flowrate of 19 l/s was about 39% of the nominal capacity of 68.4 m3/h, corresponding to Re=29.000, defined as ${\displaystyle {Re=U_{av}D/\mu }}$, where ${\displaystyle {\rho }}$ denotes fluid (air) density, ${\displaystyle {U_{av}}}$is the average fluid velocity, ${\displaystyle {D=100}}$mm the inlet draft-tube diameter, and ${\displaystyle {\mu }}$ is the dynamic viscosity. The operating head was H=1.67 m and the rotating speed 2273 min-1, yielding the other two basic non-dimensional design parameters, the specific speed, ${\displaystyle {n_{s}=nP^{1/2}/H^{5/4}}}$, of about 350, and the swirl intensity ${\displaystyle {S=W_{max}/U_{max}}}$ = 0.78.

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.