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Research Papers: Flows in Complex Systems

# Experimental and Numerical Investigation of the Precessing Helical Vortex in a Conical Diffuser, With Rotor–Stator Interaction

[+] Author and Article Information

Division of Fluid Dynamics,
Department of Applied Mechanics,
Chalmers University of Technology,
Göteborg SE-412 96, Sweden

A. Bosioc

Assistant Professor
Department of Hydraulic Machinery,
University Politehnica Timişoara,
Bv. Mihai Viteazu, No. 1,
Timişoara Ro-300222, Romania
e-mail: alin.bosioc@upt.ro

H. Nilsson

Professor
Division of Fluid Dynamics,
Department of Applied Mechanics,
Chalmers University of Technology,
Göteborg SE-412 96, Sweden
e-mail: hani@chalmers.se

S. Muntean

Center for Advanced Research in
Engineering Sciences,
Bv. Mihai Viteazu, No. 24,
Timişoara Ro-300223, Romania

R. Susan-Resiga

Professor
Department of Hydraulic Machinery,
University Politehnica Timişoara,
Bv. Mihai Viteazu, No. 1,
Timişoara Ro-300222, Romania
e-mail: romeo.resiga@upt.ro

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received May 12, 2015; final manuscript received April 5, 2016; published online June 8, 2016. Assoc. Editor: Bart van Esch.

J. Fluids Eng 138(8), 081106 (Jun 08, 2016) (13 pages) Paper No: FE-15-1323; doi: 10.1115/1.4033416 History: Received May 12, 2015; Revised April 05, 2016

## Abstract

The flow unsteadiness generated in a swirl apparatus is investigated experimentally and numerically. The swirl apparatus has two parts: a swirl generator and a test section. The swirl generator which includes two blade rows, one stationary and one rotating, is designed such that the emanating flow at free runner rotational speed resembles that of a Francis hydroturbine operated at partial discharge. The test section consists of a conical diffuser similar to the draft tube cone of a Francis turbine. Several swirling flow regimes are produced, and the laser Doppler anemometry (LDA) measurements are performed along three survey axes in the test section for different runner rotational speeds (400–920 rpm), with a constant flow rate, 30 l/s. The measured mean velocity components and its fluctuating parts are used to validate the results of unsteady numerical simulations, conducted using the foam-extend-3.0 CFD code. Furthermore, phase-averaged pressure measured at two positions in the draft tube is compared with those of numerical simulations. A dynamic mesh is used together with the sliding general grid interfaces (GGIs) to mimic the effect of the rotating runner. The delayed detached-eddy simulation method, conjugated with the Spalart–Allmaras turbulence model (DDES–SA), is applied to achieve a deep insight about the ability of this advanced modeling technique and the physics of the flow. The RNG $k−ε$ model is also used to represent state-of-the-art of industrial turbulence modeling. Both models predict the mean velocity reasonably well while DDES–SA presents more realistic flow features at the highest and lowest rotational speeds. The highest level of turbulence occurs at the highest and lowest rotational speeds which DDES–SA is able to predict well in the conical diffuser. The special shape of the blade plays more prominent role at lower rotational speeds and creates coherent structures with opposite sign of vorticity. The vortex rope is captured by both turbulence models while DDES–SA presents more realistic one at higher rotational speeds.

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## Figures

Fig. 2

Sketch of the test section with survey axes W0, W1, and W2. Two wall pressure taps in draft tube: PT1 at throat and PT2 100 mm axially downstream of first tap.

Fig. 4

(a) Swirl generator delivers swirling flows similar to Francis turbine and (b) mesh configuration used by DDES–SA computations

Fig. 5

Axial, W, and tangential, U, mean velocity compared with experimental results for 400 rpm: (a) W0, 400 rpm, (b) W1, 400 rpm, and (c) W2, 400 rpm. Solid line: DDES–SA, solid line with ×: RNG k−ε, and markers: experimental results.

Fig. 6

Axial, W, and tangential, U, mean velocity compared with experimental results for 600 rpm: (a) W0, 600 rpm, (b) W1, 600 rpm, and (c) W2, 600 rpm. Solid line: DDES–SA, solid line with ×: RNG k−ε, and markers: experimental results.

Fig. 7

Axial, W, and tangential, U, mean velocity compared with experimental results for 920 rpm: (a) W0, 920 rpm, (b) W1, 920 rpm, and (c) W2, 920 rpm. Solid line: DDES–SA, solid line with ×: RNG k−ε, and markers: experimental results.

Fig. 8

Axial, wrms′, and tangential, urms′, velocity fluctuation RMS: (a) W0, 400 rpm, (b) W0, 600 rpm, (c) W0, 920 rpm, (d) W1, 400 rpm, (e) W1, 600 rpm, and (f) W1, 920 rpm. Circle line: experimental tangential, star line: experimental axial, dash: DDES–SA tangential, and solid line: DDES–SA axial.

Fig. 9

Pressure fluctuation RMS by DDES–SA, p*=prms′/ρWthroat2: (a) W0 and (b) W1. Dashed dotted: 920 rpm, solid line: 400 rpm, and × line: 600 rpm.

Fig. 11

Phase-averaged pressure at 920 rpm from PT1 and PT2 in the draft tube compared with numerical results. Three profiles of PT1 are shifted 0.01 vertical unit downward for clarity.

Fig. 12

Isosurface of pressure by ((a) 400 rpm, (c) 600 rpm, and (e) 920 rpm) RNG k−ε and ((b) 400 rpm, (d) 600 rpm, and (f) 920 rpm) DDES–SA

Fig. 13

Temporal power spectral density (PSD) versus normalized frequency for a probe at the on-axis point of W1 captured by LDA: ((a)–(c)) tangential (U-component velocity PSD) velocity component: 400 rpm, 600 rpm, and 920 rpm; ((d)–(f)) axial (W-component velocity PSD) velocity component: 400 rpm, 600 rpm, and 920 rpm

Fig. 14

Temporal PSD of axial (W-component velocity PSD) and tangential (U-component velocity PSD) velocity components versus normalized frequency for a probe at the on-axis point of W1 using DDES–SA. Straight line is Kolmogorov −5/3 slope: (a) 400 rpm, (b) 600 rpm, and (c) 920 rpm. U-component velocity PSD is shifted 100 units downward for clarity.

Fig. 15

Vorticity magnitude at three cross sections in the draft tube by DDES–SA: (a) 400 rpm, (b) 600 rpm, and (c) 920 rpm

Fig. 3

Characteristic m(q) dependence for the swirl apparatus

Fig. 1

(a) Schematic view of experimental closed-loop test rig and (b) schematic view of swirl generator

Fig. 10

Axial vorticity at two cross sections in the runner by DDES–SA (close to the leading and trailing edges): (a) 400 rpm, (b) 600 rpm, and (c) 920 rpm. α: hub effect, β: shroud effect, γ: separation at suction side, and ζ: interaction of shroud effect and the blade wake. The arrow shows how the shroud effect intensifies in the runner.

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