**1. Introduction**

The demand to control and regulate the electrical grid to provide grid stability is ever increasing. This is a consequence of the fact that intermittent renewable energy sources, e.g., wind and solar, are on the rise and will continue to increase in the coming decades [1]. Pumped Hydro Storage (PHS) is the maturest and most cost-efficient solution to store energy and thus provide grid stability [2–4]. The oldest PHS power plants date back to the late 19th Century [5]. In the year 2019, PHS had a capacity of 158 GW worldwide [3]. Traditionally, PHS facilities require very specific site locations to make them economically feasible. According to Deane et al. [6], the head of the PHS facility is the most essential criterion, and a higher head is preferable. Most research is thus focused on PHS intended for higher heads. The ALPHEUS H2020 EU project ("Augmenting Grid Stability Through Low Head Pumped Hydro Energy Utilization and Storage") aims to contribute with economically viable PHS solutions for low- to ultra-low-heads [7,8]. The main goals of the ALPHEUS project are to achieve a reversible pump-turbine with a power of 10 MW, a round-trip efficiency of 70–80%, and heads in the region of 2–20 m. The ALPHEUS project focuses on three pump-turbine designs, a shaft-driven Counter-Rotating Pump-Turbine (CRPT), a rim-driven CRPT, and a positive displacement configuration. In the present paper, a model scale of an initial design of the shaft-driven CRPT is considered.

Wintucky and Stewart [9] concluded already in the 1950s that a counter-rotating turbine may have 2–4% higher overall efficiency compared to a single-rotor configuration. The concept of a counter-rotating propeller configuration is commonly associated with marine or aeroplane propulsion systems [10]. In recent years, the counter-rotating

**Citation:** Fahlbeck, J.; Nilsson, H.; Salehi, S. Flow Characteristics of Preliminary Shutdown and Startup Sequences for a Model Counter-Rotating Pump-Turbine. *Energies* **2021**, *14*, 3593. https://doi.org/ 10.3390/en14123593

Academic Editor: Andrea De Pascale

Received: 30 April 2021 Accepted: 14 June 2021 Published: 16 June 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

propeller configuration has been investigated as a reversible hydropower pump-turbine unit. Furukawa et al. [11] stated in 2007 that a CRPT, compared to a single rotor, can have a smaller shroud diameter, a lower rotational speed, and a wider range of operation at high efficiency with an individual speed control of the two runners. In a multi-objective optimisation of a CRPT, Kim et al. [12] showed that a hydraulic efficiency of close to 80% in turbine mode and above 85% in pump mode could be achieved, for a wide range of operating conditions. A CRPT has been analysed in pump mode with unsteady Computational Fluid Dynamics (CFD) simulations and validated with experimental test data by Momosaki et al. [13]. It was concluded that unsteady computations are required to accurately predict the performance of the CRPT, even at the design point.

Recent studies of Francis-like pump-turbines have shown that it is possible to numerically predict the flow characteristics during transient sequences such as load-rejection and mode-switching [14–17]. The current study investigated the shutdown and startup sequences for a model-scale CRPT, in both pump and turbine modes. In conventional Francis-like pump-turbines, guide vanes are used to direct and control the flow [18]. In contrast to the various Francis-like pump-turbines, the shaft-driven CPRT in the ALPHEUS project has no guide vanes. It is the head and individual rotational speeds of the runners that determine the point of operation. The transient sequences include a decrease of the runner rotational speeds, from the design point to stand-still. The rotational speeds are later increased from stand-still back to the design point.

## **2. Design and Operating Conditions**

Figure 1 shows the blade geometry of the analysed CRPT, as well as the computational domain. Conventional Francis-like pump-turbines utilise guide vanes to produce angular momentum in turbine mode and to reduce angular momentum in pump mode, thus ensuring high efficiency in both modes. This is not the case for the CRPT as the basic principle of the CRPT is that the upstream runner is designed to have an axial inflow, while the counter-rotating downstream runner makes use of the angular momentum leaving the upstream runner, generating a close to axial flow downstream the runners at the best efficiency point. Figure 1a shows the blade geometries of Runner 1 (red) and Runner 2 (blue). Runner 1 worked as the upstream runner in pump mode and downstream in turbine mode. In this study, the CRPT was at model scale, since the numerical results are later to be validated against experimental test data. Figure 1b shows the full computational domain, the locations of velocity probing lines, and pressure probe P4. The computational domain included the two runners, the hub with support struts, and contraction/expansion sections before/after the machine to focus the kinetic energy. Some parts of the straight pipes were included in the computational domain to keep the boundary conditions at some distance. The total length was 12.8-times the diameter of the runners. In pump mode, the flow was from left to the right, and in turbine mode, it was from right to left.

**Figure 1.** Blade geometry and computational domain. (**a**) Runner 1 (red) and Runner 2 (blue). (**b**) Computational domain with the coordinate system, geometrical dimensions, location of pressure probe P4, and velocity lines 1 and 2. In pump mode, the flow is from left to right (positive *z*) and, in turbine mode, from right to left (negative *z*).

> The blade geometries, shown in Figure 1a, were designed by Advanced Design Technology (ADT) Ltd., as a part of the ALPHEUS H2020 EU project [19]. Runner 1 had eight blades, while Runner 2 consisted of seven blades. The two runners rotated in opposite

directions from one another. No guide vanes were utilised, as the upstream runner was designed to have an axial inflow. The runner hub and shroud diameters were 156 mm and 270 mm, respectively. The machine was operated by individually controlling the rotational speed of each runner. At the design point in pump mode, Runner 1 rotated at 1423 rpm and Runner 2 at 1307 rpm. The corresponding rotational speeds in turbine mode were 832 rpm and 749 rpm. The engineering quantities at the design point are summarised in Table 1. The net head and power were higher in pump mode since the machine must overcome the hydraulic losses at the test facility. In turbine mode, those losses were subtracted, yielding a lower net head and power. The hydraulic efficiency of the machine was roughly the same in both modes. The head was defined by the total pressure drop of the computational domains of the runners, coloured red and blue in Figure 1b. The efficiency is calculated in pump and turbine modes as:

$$
\eta\_{\text{Pump}} = \frac{\rho g H Q}{P},
\tag{1}
$$

$$
\eta\_{\text{Turbine}} = \frac{P}{\rho g H Q}.\tag{2}
$$

Here, *ρ* is the fluid density, *g* is the gravity acceleration, *H* is the head, and *P* is the power. The power was in this work defined as *P* = *T*R1ΩR1 + *T*R2ΩR2, where *T* is the torque and Ω is the rotational speed in rad/s of the runners. The subscripts R1 and R2 are for Runner 1 and Runner 2, respectively.

**Table 1.** Engineering quantities at the design point in pump and turbine modes.


#### **3. Methods**

The present CRPT was previously evaluated in detail at the design point in both pump and turbine mode, with both steady-state and unsteady numerical simulations [20]. In the present study, shutdown and startup sequences were simulated and analysed using CFD. The numerical simulations were carried out with the OpenFOAM-v1912 open-source CFD software [21,22]. As previously mentioned, the runners rotated at individual speeds. For a given net head, it was the combination of rotational speeds of the runners that controlled the operating point of the machine. Two full shutdown and startup sequences were carried out in the present work, one for each mode. The rotational speeds were first decreased, from the design point to stand-still, and later increased back to the design point. The evaluated transient sequences are shown in Figure 2. The rotational speeds are presented as functions of time for the two modes. At time *t* = 0 s, the flow was fully developed at the design point, based on the previous simulations. The shutdown sequences started at time *t*0,1 = 0.2 s in both modes. The time from the design point to complete stand-still was 2.6 s and 4.5 s in turbine and pump mode, respectively. The runners were at a stand-still between times *t*end,1 and *t*0,2. The startup sequences started at *t*0,2 and continued to *t*end,2. The entire simulation time was 8.0 s in turbine mode and 11.3 s in pump mode. The transient sequence required less time in turbine mode as the rotational speeds were lower at the design point compared to in pump mode. The rotational speeds were decreased and increased symmetrically by a sinusoidal function as:

$$m\_{\rm r} = \frac{n\_{\rm r,DP}}{2} \left[ 1 + \sin \left( \pi \frac{t - t\_0}{t\_{\rm end} - t\_0} \pm \frac{\pi}{2} \right) \right]. \tag{3}$$

Here, *n* is the rotational speed in rpm, *n*DP is the rotational speed at the design point, *t* is the time, *t*<sup>0</sup> is the start time of the transient, and *t*end is the end time of the transient. Index *r* is 1 or 2 for the corresponding runner. The ± sign is positive when decreasing the rotational speed and negative when increasing the speed. The sinusoidal shape to change the rotational speed of the runners was chosen since a sinusoidal function allows a smooth transition between two constant rotational speeds.

**Figure 2.** Rotational speeds of the runners as a function of time during the transient sequences. Here, R1 and R2 denote Runner 1 and Runner 2, respectively, *t*0,*<sup>i</sup>* and *t*end,*<sup>i</sup>* correspond to the start respective end time of the transient operation. Index *i* is 1 for shutdown and 2 for startup. (**a**) Turbine mode: *t*0,1 = 0.2 s, *t*end,1 = 2.8 s, *t*0,2 = 4.2 s, *t*end,2 = 6.8 s. (**b**) Pump mode: *t*0,1 = 0.2 s, *t*end,1 = 4.7 s, *t*0,2 = 5.8 s, *t*end,2 = 10.3 s.
