Research Papers

A Systematic Validation of a Francis Turbine Under Design and Off-Design Loads

[+] Author and Article Information
Chirag Trivedi

Waterpower Laboratory,
NTNU—Norwegian University of
Science and Technology,
Trondheim 7491, Norway
e-mail: chirag.trivedi@ntnu.no

Manuscript received May 14, 2017; final manuscript received June 3, 2019; published online June 20, 2019. Assoc. Editor: David Moorcroft.

J. Verif. Valid. Uncert 4(1), 011003 (Jun 20, 2019) (16 pages) Paper No: VVUQ-17-1018; doi: 10.1115/1.4043965 History: Received May 14, 2017; Revised June 03, 2019

Computational fluid dynamic (CFD) techniques have played a significant role in improving the efficiency of the hydraulic turbines. To achieve safe and reliable design, numerical results should be trustworthy and free from any suspicion. Proper verification and validation (V&V) are vital to obtain credible results. In this work, first we present verification of a numerical model, Francis turbine, using different approaches to ensure minimum discretization errors and proper convergence. Then, we present detailed validation of the numerical model. Two operating conditions, best efficiency point (BEP) (100% load) and part load (67.2% load), are selected for the study. Turbine head, power, efficiency, and local pressure are used for validation. The pressure data are validated in time- and frequency-domains at sensitive locations in the turbine. We also investigated the different boundary conditions, turbulence intensity, and time-steps. The results showed that, while assessing the convergence history, convergence of local pressure/velocity in the turbine is important in addition to the mass and momentum parameters. Furthermore, error in hydraulic efficiency can be misleading, and effort should make to determine the errors in torque, head, and flow rate separately. The total error is 9.82% at critical locations in the turbine. The paper describes a customized V&V approach for the turbines that will help users to determine total error and to establish credibility of numerical models within hydraulic turbines.

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Grahic Jump Location
Fig. 1

Experimental setup of a model Francis turbine. The circular ring manifold was used to acquire the inlet and outlet pressure of the turbine.

Grahic Jump Location
Fig. 2

Locations of pressure sensors in the turbine. Sensors R1–R4 are in the runner; DT1–DT4 are in the draft tube cone; VL1 and VL2 are in the vaneless space.

Grahic Jump Location
Fig. 3

Hexahedral mesh of the model Francis turbine with labyrinth seals. The right-top, - right-middle, and right--bottom figures correspond to zoomed-in views of the blade leading edge, upper labyrinth and lower labyrinth, respectively.

Grahic Jump Location
Fig. 4

Computational domain of a Francis turbine considered for the numerical simulations. Labyrinth seals are not shown.

Grahic Jump Location
Fig. 5

Mesh convergence study of the efficiency, torque, head, and pressure in the turbine. The mesh densities m1 and m4correspond to 9 × 106 and 30 × 106 nodes, respectively. The pressure in the vaneless space, runner, and draft tube correspond to the point locations on the no-slip boundary.

Grahic Jump Location
Fig. 6

Relative error in the power values computed using the whirl component at the runner inlet and outlet (see Eq. (15)). m1 is the coarse mesh, with 9 × 106 nodes, and m4 is the fine mesh, with 30 × 106 nodes.

Grahic Jump Location
Fig. 7

The effect of the temporal discretization in the runner of a high-head Francis turbine at the BEP. The pressure variation corresponds to the guide vane passing frequency and the amplitudes at the blade leading edge.

Grahic Jump Location
Fig. 8

Iterative convergence of pressure values at the casing inlet (SC), vaneless space (VL1), runner (R1), and draft tube (DT1) during BEP. Cp = (p − pref)/(0.5 ρu2).

Grahic Jump Location
Fig. 9

Time-average validation of the pressure data at six locations inside the turbine. êitr=(pexp − pnum) × 100/pexp.

Grahic Jump Location
Fig. 10

Unsteady pressure (head) fluctuations in the vaneless space (VL1), runner (R2) and draft tube (DT1) under the BEP (left) and PL (right) operating conditions. The x-axis scale for DT1 PL and the y-axis scale for all plots are different to ensure a clear visualization of the fluctuations.

Grahic Jump Location
Fig. 11

Validation of numerical pressure data in the vaneless space (VL1), runner (R2) and draft tube (DT1) under the BEP (right) and PL (left) operating conditions

Grahic Jump Location
Fig. 12

Validation of the pressure amplitudes in the vaneless space (VL1), runner (R2), and draft tube (DT1) using power spectral analysis under the BEP (right) and PL (left) operating conditions. fb, fgv, and frh are the blade passing, guide vane passing and vortex rope frequencies, respectively. On the x-axis, the frequencies are normalized by the runner rotational speed, i.e., 5.5 Hz.



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