## ABSTRACT

To gain a comprehensive understanding of the energy dissipation of a double-suction pump, analysing the energy loss of its various components is necessary. However, the liquid temperature in the double-suction pump remains almost constant, using the entropy production or dissipation method to evaluate energy loss is difficult. The traditional analysis method based on pressure drop cannot quantify the internal energy changes in each component. To solve this problem, a pressure energy loss evaluation approach is developed on the basis of the pressure drop theoretical analysis and numerical prediction, and the effects of cavitation on the energy loss are investigated. The structure of the volute casing is improved to enhance the performance based on energy loss analysis and cavitation behaviour prediction. The results show that the energy loss efficiencies for the suction casing, impeller, and volute casing are 0.55, 4.6, and 5%, respectively, at the design flow rate. The proportion of energy loss in the impeller and volute casing increased with a decrease in NPSHa. The RNG *k*–*ε* and *k*–*ω* turbulence models are chosen for the numerical simulation, and the numerically predicted results are verified experimentally.

## HIGHLIGHTS

A pressure energy loss evaluation approach for a double-suction pump is developed.

The effects of cavitation on energy consumption are analysed.

Two turbulence models of RNG

*k*–*ε*and*k*–*ω*are used for numerical simulation.Energy changes within the component for double-suction pump are revealed.

Experiments are performed to verify the accuracy of the numerical model.

## NOMENCLATURE

*B*_{im}impeller outlet width (mm)

*D*_{im}impeller diameter (mm)

*D*_{imn}impeller inlet diameter (mm)

*D*_{in}pump inlet diameter (mm)

*D*_{out}pump outlet diameter (mm)

approximate relative error (%)

extrapolated relative error (%)

*F*_{cond}empirical calibration parameters of condensation

*F*_{vap}empirical calibration parameters of evaporation

*H*head (m)

*g*gravitational acceleration (m·s

^{−1})fine-grid convergence index (%)

*m*^{+}mass transfer source terms of evaporation

*m*^{−}mass transfer source terms of condensation

*M*torque (N·m)

*n*speed (r·min

^{−1})*n*_{s}specific speed

*N*total number of cells used for the simulation

*p*pressure (Pa)

*p*_{im_in}total pressure at the inlet section of the impeller (Pa)

*p*_{im_out}total pressure at the outlet section of the impeller (Pa)

*p*_{in}total pressure at the inlet of the pump (Pa)

*p*_{out}total pressure at the outlet of the pump (Pa)

*p*_{su_in}total pressure at the inlet section of the suction casing (Pa)

*p*_{su_out}total pressure at outlet section of the suction casing (Pa)

*p*_{v}vapour pressure (Pa)

*p*_{vo_in}total pressure at the inlet section of the volute casing (Pa)

*p*_{vo_out}total pressure at outlet section of the volute casing (Pa)

*Q*flow rate (m

^{3}·h^{−1})*Q*_{d}design flow rate (m

^{3}·h^{−1})*R*_{B}radius of a nucleation site (m)

*u*velocity (m·s

^{−1})*u*_{in}inlet velocity of pump (m·s

^{−1})*ΔV*_{i}volume of the

*i*-th cell*Z*blade number

### Greek Letters

*α*_{nuc}nucleation site volume fraction

*α*_{v}vapour volume fraction

*μ*_{l}liquid dynamic viscosity (Ns·m

^{−2})*μ*_{m}mixture of dynamic viscosity (Ns·m

^{−2})*μ*_{t}turbulent viscosity (Ns·m

^{−2})*μ*_{v}vapour dynamic viscosity (Ns·m

^{−2})*ρ*_{l}liquid density (kg·m

^{−3})*ρ*_{m}mixture of density (kg·m

^{−3})*ρ*_{v}vapour density (kg·m

^{−3})*ω*angular velocity (rad·s

^{−1})*η*efficiency

*η*_{im}impeller loss efficiency

*η*_{su}suction casing loss efficiency

*η*_{vo}volute casing loss efficiency

## INTRODUCTION

Double-suction centrifugal pumps have a high flow rate and are utilised extensively in various areas such as water supply systems, the energy industry, and agriculture. The energy used by pumps accounts for nearly 22% of the total energy consumed by electric motors worldwide (Kalaiselvan *et al.* 2016; Wang *et al.* 2017; Gan *et al.* 2022; Wang *et al.* 2023), which means that pumps have great potential for energy savings. The structure of a double-suction pump is more complex than that of a single-stage centrifugal pump and usually has a semi-spiral-type suction casing. To gain a comprehensive understanding of the energy dissipation of a double-suction pump, analysing the energy loss of its various components is necessary.

Numerous analytical and experimental studies have been conducted to analyse the energy losses of pumps or pumps operating in turbine modes. Zhang *et al.* (2018), Li *et al.* (2020), and Chen *et al.* (2022) used the particle image velocimetry (PIV) technique to explain the flow pattern in pumps, described the velocity evolution for different flow rates in the impeller, and analysed the energy conversion characteristics. Huan *et al.* (2021) conducted a visual experiment using a high-speed camera to investigate the progression of cavitation in an inducer-equipped high-speed centrifugal pump and performed a numerical simulation to analyse the alterations in flow patterns caused by cavitation. However, the PIV measurement technique requires certain parts of the pump to be transparently visible and then combined with a high-speed camera for experiments, which limits its application.

Entropy production or dissipation is commonly used to assess the energy loss of a pump. For instance, Hou *et al.* (2016a) and Wang *et al.* (2019) adopted an entropy production method to analyse the energy loss of a cryogenic submerged pump for liquefied natural gas (LNG) and investigated the internal flow conditions and distribution of the entropy production rate. Lin *et al.* (2021) adopted the entropy dissipation method to assess the energy loss of a centrifugal pump used as a turbine and studied the entropy dissipation component under variable working conditions. Li *et al.* (2018) analysed the cavitation head-drop characteristics of a centrifugal pump using the entropy generation method and described the vapour distribution and entropy generation rate. However, double-suction centrifugal pumps are typically used as front pumps for high-pressure boiler water supply systems, and the temperature in the pump remains almost constant. Therefore, using the entropy production or dissipation method to evaluate energy loss is difficult.

Previous studies used pressure energy dissipation to predict the loss of each component of a centrifugal pump. Hou *et al.* (2016b) examined the effects of a radial diffuser while analysing the energy loss of a double-suction centrifugal pump. Hou *et al.* (2017) and Wang *et al.* (2019) compared the values of the entropy production energy loss and pressure energy loss of pumps and observed little difference between the two methods. However, these studies focused on the total energy loss in the pump component and did not analyse the energy changes within each component. In addition, the turbulence model is critical in the energy loss simulation of a pump, and a reasonable turbulence model can improve the calculation accuracy. Moreover, RNG *k*–*ε* (Xu *et al.* 2016; Tang *et al.* 2017; Song *et al.* 2018; Quan *et al.* 2020; Yan *et al.* 2020; Zhang *et al.* 2023) and *k*–*ω* (Li *et al.* 2019, 2021; Wang *et al.* 2020) are commonly used turbulence models, but few studies have focused on the differences between the two models.

Cavitation may lead to the degradation of pump performance, vibration, noise, and erosion (Al-Obaidi 2020a, 2020b; Al-Obaidi & Mishra 2020), which often occurs with a vapour region attached to the impeller blades, where the region grows as the pump inlet pressure decreases. Several studies have been conducted to understand and explain the cavitation characteristics. Tao *et al.* (2018) examined the cavitation behaviour of a reversible pump turbine in pump mode along with the characteristics of critical and inception cavitation. Zhu *et al.* (2021) examined the effects of leading-edge cavitation on the axial force of an impeller blade in the pump of a reversible pump turbine and found that the axial force first increased and then decreased. Fan *et al.* (2022) studied the cavitation behaviour of liquid nitrogen inducers at various rotating speeds and inlet temperatures and developed a theoretical prediction method to predict cavitation performance. Cavitation characteristics have been extensively studied by previous investigators. However, studies on the effects of cavitation on the energy loss of pumps are rare. Although Shi *et al.* (2021) revealed the effects of cavitation evolution on the energy conversion characteristics of a multiphase pump, no energy loss analysis has been conducted for each component of the pump.

In this study, a pressure energy loss evaluation approach for a double-suction pump is proposed that is easier to implement and has a wider range of applications. The RNG *k*–*ε* and *k*–*ω* turbulence models are used to predict the pump performance, and the differences between the two models are investigated. The energy loss and internal changes in each component at different flow rates are analysed numerically, and the effects of cavitation on energy consumption are investigated. The numerically predicted results are verified experimentally. In addition, the structure of the volute casing is improved to enhance the performance based on energy loss analysis and cavitation behaviour prediction.

## MACHINE DESCRIPTION AND EXPERIMENTAL TESTS

Parameters . | Values . | Parameters . | Values . |
---|---|---|---|

Flow rate Q_{d} (m^{3}·h^{−1}) | 1,300 | Pump outlet diameter D_{out} (mm) | 375 |

Head H (m) | 14 | Blade number Z | 6 |

Speed n (r·min^{−1}) | 970 | Impeller diameter D_{im} (mm) | 380 |

Specific speed n_{s} | 293.96 | Impeller inlet diameter D_{imn} (mm) | 262 |

Pump inlet diameter D_{in} (mm) | 450 | Impeller outlet width B_{in} (mm) | 101.25 |

Parameters . | Values . | Parameters . | Values . |
---|---|---|---|

Flow rate Q_{d} (m^{3}·h^{−1}) | 1,300 | Pump outlet diameter D_{out} (mm) | 375 |

Head H (m) | 14 | Blade number Z | 6 |

Speed n (r·min^{−1}) | 970 | Impeller diameter D_{im} (mm) | 380 |

Specific speed n_{s} | 293.96 | Impeller inlet diameter D_{imn} (mm) | 262 |

Pump inlet diameter D_{in} (mm) | 450 | Impeller outlet width B_{in} (mm) | 101.25 |

## NUMERICAL METHODS

Steady simulations were carried out utilising the ANSYS CFX 18.0 flow solver, and both RNG *k–ε* and *k–ω* turbulence models were used for numerical simulation. Since the *k–ω* and RNG *k–ε* turbulence models are widely used in the low specific speed centrifugal pumps, and RNG *k–ε* turbulence model can accurately predict the rotating and curvature flow in the flow passage components. Moreover, two models are verified by a large amount of previous work (see Section 1). The effects of cavitation can be disregarded because the total pressure at the pump inlet throughout the test was at atmospheric pressure.

*H*and efficiency

*η*.where

*p*

_{in}and

*p*

_{out}are the total pressure at the pump's inlet and outlet,

*g*is the gravitational acceleration,

*Q*is the flow rate,

*M*is the torque, and

*ω*is the angular velocity.

### Physical model and setting up

#### Physical model and mesh

*D*

_{in}and 6

*D*

_{out}, respectively.

#### Numerical setup

At the inlet section of the suction casing, the total pressure was given, whereas for the outlet section of the volute casing, the mass flow rate was in the range of 0.2–1.4 *Q*_{d}. The reference pressure was set to 0 atm. For a proper connection, the interface was adopted in the fluid–fluid domain, and the interfaces between the impeller and stationary components were taken as a frozen rotor. The rotational speed of the impeller was specified in a rotating frame of reference, whilst the suction and volute regions were set as stationary. The boundary walls were modelled using a non-slip smooth wall condition. The maximum number of iterations was set as 3,500 and the residual value of the convergence criteria was 1 × 10^{−4}.

### Mesh-independence study and uncertainty analysis

The inlet and outlet extensions were modelled together with the suction and volute casings, respectively; therefore, they were also meshed together. As listed in Table 2, Case A was used as the initial mesh for the mesh-independence study under a total mesh size of 2,810,586. The mesh was further improved to investigate its effect on the numerical results. The mesh numbers for Cases B–E were 1.16, 1.31, 1.58, and 1.83 times that of Case A, respectively. The predicted head *H* changed significantly from Case A to D as the mesh size increased, and slightly from Case D to E. Therefore, mesh D was deemed appropriate and utilised throughout the study.

Case . | Mesh elements . | H (m)
. | Error (%) . | |||
---|---|---|---|---|---|---|

Suction casing and inlet extend . | Impeller . | Volute casing and outlet extend . | Shroud chamber . | |||

A | 815,520 | 1,091,304 | 670,854 | 232,908 | 13.85 | – |

B | 886,145 | 1,255,612 | 839,344 | 279,489 | 14.21 | 2.53 |

C | 998,756 | 1,411,855 | 959,645 | 299,553 | 14.59 | 2.6 |

D | 1,009,962 | 1,988,820 | 1,123,522 | 329,508 | 14.8 | 1.42 |

E | 1,278,797 | 2,187,709 | 1,280,815 | 395,417 | 14.73 | 0.47 |

Case . | Mesh elements . | H (m)
. | Error (%) . | |||
---|---|---|---|---|---|---|

Suction casing and inlet extend . | Impeller . | Volute casing and outlet extend . | Shroud chamber . | |||

A | 815,520 | 1,091,304 | 670,854 | 232,908 | 13.85 | – |

B | 886,145 | 1,255,612 | 839,344 | 279,489 | 14.21 | 2.53 |

C | 998,756 | 1,411,855 | 959,645 | 299,553 | 14.59 | 2.6 |

D | 1,009,962 | 1,988,820 | 1,123,522 | 329,508 | 14.8 | 1.42 |

E | 1,278,797 | 2,187,709 | 1,280,815 | 395,417 | 14.73 | 0.47 |

*y*+ requirements for accurate predictions of the near-wall flow. In general, the maximum value of the

*y*+ in the water pump is less than 300 for a two-equation turbulence model, such as the

*k*-epsilon or

*k*-omega model (Wei

*et al.*2019; Wang 2020). The

*y*+ of the impeller is displayed in Figure 6. The largest value of

*y*+ was below 150, which satisfies the minimum requirement of the wall function used in the simulation.

*et al.*2013; Zhao

*et al.*2020). Three sets of mesh sizes with A (2,810,586), C (3,669,809), and D (4,451,812) elements were chosen for the numerical accuracy analysis. The static pressure of two monitor points in the volute casing was selected as the ‘variable

*φ*’ at a flow rate of 1.1

*Q*

_{d}(see Figure 7). The mesh size

*h*is defined aswhere Δ

*V*is the volume of the

_{i}*i*-th cell and

*N*is the total number of cells used for the simulation. The apparent order

*p*

_{ao}of the estimation method can be written as

The errors for monitor points 1 and 2 can be obtained by the above equations, and the results are shown in Table 3. Hence, the numerical uncertainty in the fine-grid solution for the reattachment length should be reported as 2.095%.

Parameters . | φ = static pressure of P_{1}/P_{a}
. | φ = static pressure of P_{2}/P_{a}
. |
---|---|---|

N_{D}, N_{C}, N_{A} | N_{D} = 4,451,812, N_{C} = 3,669,809, N_{A} = 2,810,586 | |

r_{CD} | 1.0665 | |

r_{AC} | 1.0930 | |

φ_{D} | 233,696 | 213,102 |

φ_{C} | 232,823 | 212,361 |

φ_{A} | 231,154 | 211,078 |

p_{ao} | 4.2047 | 2.9306 |

236,504.05 | 216,670.46 | |

0.374% | 0.348% | |

1.187% | 1.647% | |

1.504% | 2.095% |

Parameters . | φ = static pressure of P_{1}/P_{a}
. | φ = static pressure of P_{2}/P_{a}
. |
---|---|---|

N_{D}, N_{C}, N_{A} | N_{D} = 4,451,812, N_{C} = 3,669,809, N_{A} = 2,810,586 | |

r_{CD} | 1.0665 | |

r_{AC} | 1.0930 | |

φ_{D} | 233,696 | 213,102 |

φ_{C} | 232,823 | 212,361 |

φ_{A} | 231,154 | 211,078 |

p_{ao} | 4.2047 | 2.9306 |

236,504.05 | 216,670.46 | |

0.374% | 0.348% | |

1.187% | 1.647% | |

1.504% | 2.095% |

## RESULTS AND DISCUSSIONS

### Numerical accuracy validation

*H*and efficiency

*η*at the design speed of 970 r·min

^{−1}. To consider the uncertainty of sensors, the pump outlet pressure

*p*

_{out}= (

*p*

_{out m}± 0.0015) MPa, inlet pressure

*p*

_{in}= (

*p*

_{in m}± 0.00025) MPa, flow rate

*Q*=

*Q*

_{m}(1 ± 0.003), and power

*P*=

*P*

_{m}(1 ± 0.005). Hence, the head

*H*and efficiency

*η*can be written asand

The findings demonstrate that the error of the *k–ω* model was higher than that of the RNG *k*–*ε* model, particularly under small flow conditions. Thus, for this investigation, the RNG *k–ε* model was used. At various flow rates, the *H* and *η* predicted by the RNG *k–ε* model agreed well with the experimental findings. As the flow rate increased, the head decreased, and the numerical results were larger than the experimental results at high flow rates. However, the experimental values were greater at low flow rates. As the flow rate increased, the efficiency first increased and then decreased, and the optimal efficiency point was at the design flow rate for both the test and simulation results. The discrepancies between the test and numerical values were within 5% at each flow rate, thereby validating the numerical method.

### Energy loss analysis

*p*

_{im_in}and

*p*

_{im_out}represent the total pressure at the inlet and outlet sections of the impeller. The pressure can be obtained by the function calculator in the CFX-Post, and the ‘Total Pressure in Stn Frame’ was used for this study.

*p*

_{su_out}and

*p*

_{su_in}are the total pressure at the outlet and inlet sections of the suction casing,

*p*

_{vo_out}and

*p*

_{vo_in}represent the total pressure at the outlet and inlet sections of the volute casing.

^{3}·h

^{−1}, and this study used a flow rate in the range of 780–1,820 m

^{3}·h

^{−1}(0. 6–1.4

*Q*

_{d}) as the study object. According to Equations (3)–(5), the energy loss of each component can be obtained (see Figure 9). Excluding the design flow rate, the energy loss of the impeller was greater than that of the suction and volute casings, whereas the energy loss of the suction casing was the lowest. The energy loss of each component was the lowest at the design flow rate and increased as the flow rate increased/decreased, particularly for the impeller.

### Suction casing and volute casing

Items . | Inlet (%) . | Transition (%) . | Semi-spiral (%) . | Spiral (%) . | Outlet (%) . |
---|---|---|---|---|---|

0.6Q_{d} | 0.009 | 0.044 | 3.985 | 5.855 | 0.331 |

0.8Q_{d} | 0.02 | 0.078 | 1.4 | 5.004 | 0.544 |

Q_{d} | 0.036 | 0.119 | 0.398 | 3.473 | 1.523 |

1.2Q_{d} | 0.059 | 0.197 | 0.692 | 2.496 | 2.365 |

1.4Q_{d} | 0.1 | 0.332 | 1.128 | 4.873 | 3.012 |

Items . | Inlet (%) . | Transition (%) . | Semi-spiral (%) . | Spiral (%) . | Outlet (%) . |
---|---|---|---|---|---|

0.6Q_{d} | 0.009 | 0.044 | 3.985 | 5.855 | 0.331 |

0.8Q_{d} | 0.02 | 0.078 | 1.4 | 5.004 | 0.544 |

Q_{d} | 0.036 | 0.119 | 0.398 | 3.473 | 1.523 |

1.2Q_{d} | 0.059 | 0.197 | 0.692 | 2.496 | 2.365 |

1.4Q_{d} | 0.1 | 0.332 | 1.128 | 4.873 | 3.012 |

*Q*

_{d}for the entire volute casing. However, vortices were present at the outlet under

*Q*

_{d}and 1.2

*Q*

_{d}flow rate conditions. This also explains why the energy loss increased in the outlet at high flow rates. As the flow rate increased, the total pressure distribution in the volute casing tended to fall in the symmetry plane, as shown in Figure 13(b). The results indicated that the design of the volute casing deviated slightly from the flow condition of

*Q*

_{d}, which could be corrected by adjusting the angle of the volute outlet.

For the suction casing and volute casing, the energy loss caused by flow mainly occurred in the near-wall region, indicating that energy loss is closely related to the shape of the casing when there is no vortex exists. However, the energy loss has increased significantly with the generation of vortex. Hence, the design principle of the suction casing and volute casing is to reduce the generation of vortex.

### Impeller

*Q*

_{d}, which explains the impeller's significantly increased energy loss at low rates. The streamline was relatively smooth at the intended flow rate

*Q*

_{d}and at a higher flow rate of 1.2

*Q*

_{d}. With an increase in the flow rate, the impeller flow velocity increased gradually from the impeller's inlet to its outlet, as shown in Figure 16(a). As the flow rate increased, the impeller's total pressure decreased and then increased from the impeller inlet to its outlet, as shown in Figure 16(b).

### Cavitation performance analysis

*et al.*2004) was selected, which considers the effects of bubble dynamics. The cavitation behaviour is more serious at a low flow rate for the double-suction pump for water supply systems. Therefore, a cavitation investigation for the double-suction pump at a flow rate of 0.772

*Q*

_{d}was conducted, as shown in Figure 17.

*NPSH*

_{3%}denotes a head drop of 3%, which is indicative of cavitation behaviour. The results of the numerical prediction were in good agreement with the data that have been measured, where the maximum error for the head was within 4% and was equal to 0.45 m for

*NPSH*

_{3}%.

*NPSHa*. The cavitation region gradually migrated from the inlet edge of the blade to the middle area as

*NPSHa*decreased, and the vapour volume fraction increased. Due to the low pressure on the suction surfaces of the blade, the bubbles were mainly concentrated on these surfaces. However, the pressure surfaces did not experience cavitation. The overall cavitation region and squeeze effect were both relatively small when

*NPSHa*= 5.24 m. As

*NPSHa*decreased to 3.2 m, numerous bubbles developed in the double-suction impeller, and the squeeze effect was more obvious.

### Energy loss optimisation

A previous energy loss and cavitation performance analysis revealed that the volute casing accounts for too much of the energy loss. The volute casing loss is greater than that of the impeller, which is unreasonable. Vortices at the outlet of the volute casing contribute considerably to the energy loss. To mitigate the effects of these vortices, the inclination angle of the volute outlet was optimised, and the best inclination value was 8° away from the volute tongue.

*H*and efficiency

*η*before and after optimisation. The figure shows that

*H*and

*η*increased under each flow rate after optimisation, particularly at high flow rates. At a flow rate of 1.4

*Q*

_{d}, the values of

*H*and

*η*exhibited the largest increases of 0.89 m and 3.36%, respectively. Prior to optimisation,

*H*and

*η*experienced rapid drops at flow rates of 1.2 and 1.4

*Q*

_{d}, as the energy loss of each component increased dramatically at high flow rates.

*Q*

_{d}. The changes in energy losses for the impeller and volute casing were much greater than that for the suction casing, and the maximum values were 0.98 and 2.03%, respectively, at a flow rate of 1.4

*Q*

_{d}.

## CONCLUDING REMARKS

In this study, the performance of a double-suction pump was investigated using theoretical, numerical, and experimental methods to obtain a more accurate energy loss prediction method. The conclusions are summarized as follows.

- (1)
The energy loss in the impeller was greater than those in the suction and volute casings, and the value in the suction casing was the lowest. Each component had a minimal energy loss at the intended flow rate, which increased as the flow rate increased/decreased, particularly for the impeller.

- (2)
For the suction casing, the energy losses in the inlet and transition parts increased as the flow rate increased, accounting for a small proportion of the total loss. For the volute casing, the energy loss in the spiral part was significantly greater than that in the outlet part at a low flow rate. However, the energy losses in the spiral and outlet parts were nearly identical at the design/high flow rate, indicating that vortices or flow separation occurred in the outlet part. For the impeller, the average total pressure increased uniformly for Sections S9–S12, and the growth rate decreased for Sections S12–S14. The average total pressure of Sections S14–S15 decreased slightly.

- (3)
The proportion of energy loss in the suction casing changed slightly before and after cavitation. However, the proportion of the impeller and volute casing increased with a decrease in

*NPSHa*, and the loss in the impeller increased at a faster rate than that in the volute casing. The cavitation region gradually migrated from the inlet edge of the blade to the middle area as*NPSHa*decreased and the vapour volume fraction increased. Due to the low pressure of the suction surfaces of the blade, the bubbles were mainly concentrated on these surfaces, and the pressure surfaces did not experience cavitation. - (4)
With the angle of the volute outlet part inclined 8° away from the volute tongue,

*H*and*η*increased, and each component's energy loss decreased. The changes in the energy losses for the impeller and volute casing were much greater than that for the suction casing, and the maximum values were 0.98 and 2.03%, respectively, at a flow rate of 1.4*Q*_{d}.

## ACKNOWLEDGEMENTS

This work was supported by National Key Research and Development Program of China (Grant No. 2022YFB4003404).

## DATA AVAILABILITY STATEMENT

Data cannot be made publicly available; readers should contact the corresponding author for details.

## CONFLICT OF INTEREST

The authors declare there is no conflict.