Recent studies have evaluated the feasibility of using pumps as turbines. Pugliese et al. investigated vertical-axis pumps running in reverse [34], while Abazariyan et al. determined the effect of viscosity on the performance of the system [35]; in turn, Kramer et al. [36] designed predictive methods to establish the optimal operating point of a pump working as turbine. This is possible because centrifugal pumps are machines that convert the mechanical energy of the shaft into hydraulic energy, thus allowing the working fluid to undergo velocity and pressure conditions according to the requirements of the system. Additionally, these devices are physically and hydraulically similar to Francis turbines, which convert the potential energy stored in water into kinetic energy in the shaft to later produce electrical energy by means of a generator [37]. Pumps can “run backward”, even to the extent of developing a certain momentum if the pressure is sufficiently high as to exceed the starting torque of the impeller and the shaft; for that reason, they can be used to generate electrical energy [38]. Therefore, PATs are pumps that could operate as reaction turbines (similar to Francis and Kaplan turbines) and generate electrical energy if connected to a generator [39].

[Figure 1] illustrates the basic concept of a centrifugal pump, working as a pump and as a turbine. The main components of this hydraulic device are the volute, impeller, and the shaft; they are responsible for generating or receiving the pressures that are necessary to make it work. [Figure 1a] presents the machine working as a pump, where its boundary values are defined by its inlet (suction) and outlet (discharge). As a result, it turns the mechanical energy of the impeller into pressure (head) and kinetic energy (flow). [Figure 1b] shows the difference in flow direction between a radial-flow pump and the pump as turbine. In the latter, the PAT transforms pressure and kinetic energy into mechanical energy applied on the shaft.

Figure 1

Scheme of a centrifugal pump: a) cross-section of the system working as a pump and b) schematic view of the device operating in turbine mode [39]

Several types of pumps can be used as PATs; classified according to the orientation of the flow through the impeller, they are generally divided into radial, mixed, and axial flow pumps. Another feature is defined by the geometry of the volute and the number of impellers attached to the shaft; therefore, they are further categorized as single, double, or multi-stage pumps.

The specific speed number, N_s, is a characteristic coefficient derived from the similarity conditions which allow a comparison of impellers of various pump sizes even when their operating data differ. As shown in eq. (1) the definition of the specific speed of the pump is:

$N_{\text{s}}=N\frac{\sqrt{Q}}{\sqrt[4]{H^3}},$ (1)

where are: N - the rotational speed (RPM); Q (m³/s)- volumetric flow rate and H (m)- net head, at the best efficiency point (BEP). This equation is used for both the turbine and pump modes of operation.

[Figure 2] presents three types of a single stage centrifugal pumps working as turbines. The relationship between the inlet diameter (D₁) and outlet diameter (D₂) of a centrifugal pump depends on the specific speed (N_s). Radial-flow pumps are subdivided for high, medium, and low head impellers, and their N_s ranges from 10 to 80, depending on the operating conditions (H). Mixed-flow pumps operate at N_s up to 160, and their axial-flow counterparts do so in a range of N_s from 140 to 400.

Figure 2

Scheme of different types of pumps used as PATs

Due to the dynamic similarity of the fluid flow in single stage PATs and Francis turbines, this study is based on the analysis of the latter. Most studies in the literature use PATs that implement single stage centrifugal pumps because of their versatility: they are compatible with a wide range of heads and flow rates and their implementation and acquisition costs are low.

Jain and Patel [Error! Bookmark not defined.] listed different methods to select PATs. They established several selection criteria: available head range, flow range, back pressure at turbine outlet, and desired speed, among others. Nevertheless, they can be reduced to three design criteria: net head (H); volumetric flow rate of the fluid (Q), and hydraulic efficiency (η) of the pump. The head represents the equivalent, in height, of the energy exchanged between the fluid and the impeller. The flow rate describes the volume of the fluid per unit of time that circulates through a section transversal to the flow. In addition, hydraulic efficiency is understood as the relationship between the energy extracted by the PAT represented by shaft power output (P) and the energy available in the fluid (ρgQH), which is calculated using eq. (2), where ρ denotes the density of the fluid and g, the gravitational acceleration [40]:

$P=\eta \rho gQH$ (2)

An early work that focused on the adequate selection of a PAT as a function of the flow conditions (Q and H) available on site was presented by Chapallaz et al. [41]. They designed a range of application of different PAT types ([Figure 3]) that enables to estimate a range of hydraulic power available at the inlet between 1 and 1000 kW, without considering losses in the system. The sections with an open area—radial, mixed, and axial—are regions where studies are needed to define the full range of action of this type of PATs. Most studies on PATs start at 1 kW of hydraulic power. The shaded regions (multistage radial and double flow pumps) are the most extensively studied types of pump, which are commercially used to generate electricity at pumped-storage plants. This has enabled to completely define (demarcate) the performance area in the guide. In a more recent work, Orchard and Klos [39] proposed more conservative operating ranges for PATs, from 5 kW to 750 kW.

Figure 3

General range of application of different PAT types proposed by Chapallaz, Eichenberg, and Fisher for suitable selection of MHP [41]

In turn, Kaunda et al. [42] established an alternative method to select a turbine for particular head and flow rate (Q and H) conditions available on site and this process is summarized in the flow chart in [Figure 4]. Besides considering hydraulic parameters to select the PAT, the said method ensures the evaluation of other important factors that can have an impact on the project, such as investment and energy generation costs, the complexity of the design, and the feasibility of the Micro Hydropower Plant (MHP) project.

Figure 4

Turbine selection flow chart for a MHP [42]

Barbarelli et al. [43] established a methodology for the selection of the PAT applied in MHP by means of a statistical numerical method. This research suggests, first, knowing the hydraulic data of the site where it will be installed regarding head (H_site) and flow (Q_site); afterwards, the rotational speed (N) of a commercial pump is assumed, in this case 2950 rpm. With the previous data, it is possible to obtain the specific speed of the site, which matches with the specific speed in turbine mode (N_st) as defined in equation 1. H_site will be equal to H_T as Q_site to Q_T, as showed in [Figure 5]. Several researchers studied the relationship between the BEP in turbine and pump mode, since they differ in terms of H and Q, establishing two conversion factors h (3) and q (4), which depend on the head and flow values at their maximum efficiency point and operation mode (H_T,BEP, H_p,BEP, Q_T,BEP, Q_p,BEP).

$h=\frac{H_{\text{T},\text{BEP}}}{H_{\text{p},\text{BEP}}}$ (3)

$q=\frac{Q_{\text{T},\text{BEP}}}{Q_{\text{p},\text{BEP}}}$ (4)

Figure 5

PAT selection procedure - flow chart for a MHP [43]

After having N_st, specific speed (N_sp) in pump mode is achieved by means of a linear correlation. There are various methods available in literature to calculate N_sp in terms of N_st. The historical correlation is summarized in Table 1.

It can be inferred from these correlations that the lowest N_sp range investigated is presented by Derakhshan [49], while the correlation with more experimental validation is presented by Barbarelli [43] with 27 hydraulic tests. Besides, the studies conducted to determine these correlations have used a N_sp lower than 80, meaning that they are radial-flow PAT, which encourages different researchers to explore correlations with axial and mixed PAT to obtain a more comprehensive overview of the single stage PAT types.

There are various methods available in literature to select q and h, based on theoretical and experimental research. The most commonly used methods to obtain coefficients are summarized in Table 2.

Derakhshan et al.[49] and Tan et al. [46] introduced a method based on theoretical analysis to evaluate the BEP. This method is based on the geometrical (Diameter) and hydraulic characteristics of the pump in direct and turbine mode.

Barbarelli et al. [43] proved their methodology thanks to a case study on possible PAT installation in Calabrian water purifier plants of Casali and Sersale (Italy). Depending on the conditions of the site and the design of the system, the Italian government established an incentive for the development of strategies that implement the use of renewable energy equivalent to 0.2 EUR/kWh. This policy results in around 25,000 EUR/year for Casali and 55,000 EUR/year for Sersale, as well as amortization periods under a year. That is a really short time for MHPs and it is an important advantage of this technology.

Commonly, studies in this field determine the dynamic response and conduct failure analyses of impellers in PATs. The impeller and the volute can resist static/dynamic pressures they were designed for, reaching up to 20 years of shelf life. Nonetheless, the complexity of the operating features when they are not working as they were designed for creates additional dynamic vibratory behaviour causing instabilities in the system; say a machine designed as a pump working in turbine mode. Fatigue failure may be associated with design problems (geometry, material, and manufacturing processes) and operating conditions that create instabilities in the flow (natural oscillation frequencies-operation) [61]. A particular study focused on the impeller of a PAT that presented a fracture during the operation while undergoing dynamic loads was performed applying the finite element method (FEM). The results of principal stress states and operating frequencies of the PAT in that work are presented in [Figure 6]. In that case, the main causes of the failure were resonance issues due to the proximity between the natural and working frequencies of the impeller and the concentration of stress as a result of the geometry of the connection between the blade and the crown [62].

Figure 6

Failure analysis of the impeller of a PAT: a) Broken impeller and start point of the crack; b) FEM results and distribution of equivalent stress [62]

Later, the same authors carried out a numerical (FEM) and experimental (EMA) study with the aim of determining the incidence of the impeller on the dynamic effects that take place inside the PAT. Their results correlate the configuration of the impeller and the failures the impeller presented, as well as the frequencies the impeller underwent and the damages caused by said frequencies [63].

S-shaped characteristics are graphs that enable to identify fluctuations in the performance of PATs. Such fluctuations are associated with transient processes, such as difficulties to synchronize with the electrical components of the turbine, pipe rupture due to excessive pressure, and load rejections, among others. [Figure 7] is a performance curve of flow rate (Ԛ_T) against efficiency (η_T) for PATs, known as S-shaped characteristic. This curve describes the conditions of stable behavior using a dotted line and the unstable performance with a solid line; the interception of the two defines the operating point of the PAT [64].

Figure 7

S-shaped characteristic curves of the PAT [65]

The main reason behind the unstable operation of PATs is pressure fluctuation. Misaligned guide vanes (MGVs) are a widely used method because they improve the S-shaped characteristic of PATs [66].

Different authors have investigated the behavior of PATs in the S-region by means of CFD simulations and assuming a stationary control volume. Liu et al. [67] carried out a numerical study into the S-shaped characteristic, and their volume control was composed of the spiral casing, stay vanes, guide vanes, impeller, and draft tube, using CFX12.1 with the SST turbulence model. Remarkably, they determined that the fluctuations generated by the instability can be mitigated using different misaligned guide vanes. Olimstad et al. [68] conducted an experimental-theoretical study and performed measurements adopting two different methods, transient sampling and throttling valves, to calculate the instabilities of the system. Both methods enabled to measure the S-shaped characteristic curves, and similar behavior was found. However, the transient method as input presented a significant standard deviation of the non-dimensional velocity at two operating points. Regarding the method with throttling valves, the authors recommend using low flow rates only because the head is drastically reduced.

Subsequently, Deyou et al. [69] carried out a numerical-experimental analysis of a 750-kW PAT based on the volume control implemented by D. M. Liu et al. in their study [67] and varied, in the numeric method, the SST turbulence model and the convergence criterion RMS_max< 10⁻⁶. This turbulence model resulted in an error below 5% compared to experimental tests, which enables to establish the validity of the numerical model they developed. Such study identified different types of vortices when the PAT enters the “S-region”. In turn, Hasmatuchi et al. [70] take the PAT to this region by experimental means because the PAT is subjected to conditions that were not considered in the design. As a result, they identified the operating conditions of the S-shaped characteristic and obtained models for different PAT prototypes, which provide static and dynamic stability criteria based on CFD simulation and its corresponding experimental validation.

Cavitation may occur in different regions of the pump when local pressure falls below the vapor pressure that corresponds to fluid temperature [71]. Turbines are prone to cavitation, mainly Francis turbines, in a very narrow range of operating conditions. In turbine mode, PATs operate similarly to Francis turbines, which may accelerate the cavitation process compared to the pump mode. Studies conducted thus far adopt two different approaches to cavitation: barotropic and bubble dynamic models. The former defines the density of the mixture based on local pressure, while the latter considers the Rayleigh–Plesse equation which governs the dynamics of a spherical bubble. These numerical models allow to predict cavitation phenomena at different operating points.

Tao et al. [72] designed a numerical-experimental model of a PAT operating as a pump. Their study highlights the measurement instruments that are necessary to capture all the cavitation effects generated by the instabilities of the system, as can be observed from [Figure 8a]. Additionally, they analyzed the way the conditions of the flow rate can cause material to be removed from the blades of the PAT. These results were experimentally validated using the measurements obtained by the equipment under different flow rate conditions and numerically evaluated by means of CFD simulations. Their study leads to conclude that cavitation areas can be predicted based on operating conditions. A later study by the same authors delved into the effect of the flow rate and its angle of incidence with respect to the blades, analyzing the velocity triangles and the formation of the associated cavitation ([Figure 8b]) [73]. Besides, Ješe and Antheaume [74] presented a similar work whose results are included in [Figure 7c], where the study variable is the net positive suction head (NSPH) and its influence on cavitation inception.

Figure 8

Test rig and experimental setup to measure cavitation inception [72]–[74]

Jintao et al. [75] evaluated the cavitation generated by an impeller of the PAT, which enabled them to compare different numerical models, such as those of mixed-flow and single stage pumps. Moreover, they were able to experimentally demonstrate that the mixed-flow model was better adapted (with an error of 5.5%), while the single stage pump reached 6.3% after its numerical method was validated.

The efficiency of PATs depends on the control of the inlet flow. However, pumps are not usually equipped with such control systems. This aspect is at the core of different studies in the field and, in that spirit, experiments have been implemented on guide blades to control the flow and evaluate the BEP of PATs in turbine mode. Giosio et al. [76] achieved an efficiency of 79%, thus reaching the same efficiency as the device in pump mode. Conversely, Sarasúa et al. [77] studied the dynamic response of PATs in SHPs and analyzed their turbine mode in depth. They analyzed two adjustment criteria to control the load by means of an automatic proportional integral (PI) control system. The first one employs the root locus analysis of the plant dynamic model, which considers the detailed effects of elasticity by means of a continuous wave model. The second one is based on a Pareto approach that finds compromise solutions between the number of oscillations and the absolute median error of the controlled variable. The two criteria are compared with the standard analog controller to optimize the generation process. This may result in an extension of the life of the plant.

Martin Polák [78] described the influence of the change of hydropower potential on PAT operation and compared the experimental results with the model of theory of physical similarity ([Figure 9a]). The model used did not include a change in efficiency similar to models of other authors who also did not consider varying efficiency. However, the results of the experimental verification proved that neglecting the variability of efficiency leads to an incorrect setting of the optimum operational parameters. This applies particularly to the flow rate and the total head dependence on shaft speed, which are the most important relationships when optimizing PAT operation. Frosina et al. [79] used three pumps of N_s 37.6, 20.5 and 64. The experiments have been performed only in steady-state conditions, varying the water flow rate and the pressure at the inlet of the pump, for different shaft speeds. In particular, the flow rate has been varied between 8 and 21 L/s, and the shaft speed between 300 and 2200 rpm. On the other hand, Ismail et al. [80] acquired the efficiency of the PAT, varying the rotational speed (N) between 800 and 1400 [rev/min] obtaining a maximum efficiency of 65.04 at 1100 [rev/min]. The experimental hydraulic system used is shown in the [Figure 9a], [b].

Figure 9

Experimental setup to determine the operating conditions: a) Courses of efficiency in modes 1-6 highlighting the optimum BEP [78]; b) Hydraulic test rig brake system and data logger; c) schematic diagram of the PAT rig [80]

Multi-objective optimization is a mathematical method that allows one to find the optimum value of a mathematical objective equation. Zhu et al. [81] used the criteria of multi-objective optimization in order to determine the incidence of geometrical parameters as blade loading, the blade lean at the high-pressure side of the impeller, and the meridional channel shape on the impeller performance. They started with reverse engineering to obtain a geometric model of the impeller and CFD simulations to estimate the objective functions and the validation of the optimization results. Subsequently, they developed a design of experiments (DOE) that determined the distribution of the sampling points in the design space. Using the root mean square (RMS), they also correlated the design parameters to the required parameters. As a result, the computational cost was significantly reduced and a PAT impeller with high BEP and operating stability was obtained.

The improvement of the performance of PATs equipped with a radial impeller has been addressed in many studies. The latter aim at determining the geometric effect of the impeller–volute assembly on the BEP of this turbomachinery. Table 3 classifies and summarizes different studies, the implemented method, where the applied methods were classified at 3 different cases; the first one is Theoretical (T), next one is Numerical (N) and the last one is Experimental (E). These geometric changes were made, such as impeller diameter (A), inlet impeller rounding (B), number of blades (C), splitter blade (D), blade wrap angle (E), blade profile (F), blade thickness (G), blade lean (H), and blade inlet angle (I).

An important result from the literature review was the finding of nine (9) geometric parameters resulting from the theoretical behavior of the optimization in pump mode, implemented also in turbine mode to analyses its influence in the efficiency of the turbomachine. These 20 researches used theoretical, numerical, and/or experimental methods. [Figure 10] describes the change of efficiency through the geometric modification of the impeller. On the abscissa, there are nine geometric parameters plus the combination of some of them, while on the ordinate, the efficiency variation regarding the original impeller is specified, finding results that increase or decrease according to the implementation of these parameters. Some of these researches resulted in a negative incidence: A, G and in some cases B, C and E. The geometric parameter with the highest incidence is D, with an increase of 4.04%, although this research only considers the numerical analysis method. Other authors use T/N/E methods such as those carried out by [98], [100], [101], which generate higher incidence, since they combine different geometric parameters to obtain favorable conditions with a maximum value of 8.07%.

Figure 10

Incidence of geometric parameters in the efficiency of PATs