ORIGINAL ARTICLE

Performance of the Centrifugal Pump of Double Suction using the Computational Fluid Dynamics Method

Ing. Ignacio David Moreno-Tamayo^I  , 0000-0001-6593-8583Dr.C. Alain Ariel de la Rosa-Andino^{II  *}  , MSc. Yusimit Karina Zamora-Hernandez^III  , 0000-0001-7456-1490Dr.C. Yoandrys Morales-Tamayo^IV  , MSc. René Misael Arias-Hidalgo^II  , 0000-0001-8553-7613MSc. Yordanka Aguilera-Corrales^II 

^IMinisterio de la Industria Alimentaria (MINAL), ASTIGOL, Manzanillo, Granma, Cuba.

^IIUniversidad de Granma, Bayamo, Granma, Cuba.

^IIIUniversidad Técnica Estatal de Quevedo. Facultad de Ciencias de la Ingeniería. Dpto. de Ingeniería Mecánica, Quevedo, Los Ríos, Ecuador.

^IVUniversidad Técnica de Cotopaxi. Facultad de Ciencias de la Ingeniería y Aplicadas. Dpto. Ingeniería Electromecánica, Extensión La Maná, Ecuador.

ABSTRACT

Centrifugal pumps of double suction are widely used in industrial and agricultural applications as their flow rate is twice that of single suction pumps with the same impeller diameter. The present work was carried out with the objective of simulating the performance of the double suction centrifugal pump BCP 125-420 by means of the Computational Fluid Dynamics method. For this, the methodological aspects to follow for the simulation and evaluation of the turbo machine operation were established using Computational Fluid Dynamics techniques and ANSYS Workbench software in version 14.5. All of this was done following the methodological recommendations referred in the literature related to the modeling of these devices. Among the main results, there is the value of the height predicted through the simulation and the real height of the pump, with magnitudes of 81,65 and 81,83 mwc, respectively; values that exceeded the 80 mca initially foreseen for the design and that allowed concluding that the error between the real height of the pump and the one obtained through the simulation did not exceed 1%, which indicated the reliability in performance of the BCP 125-420 double suction centrifugal pump under the operation conditions studied.

Key words: Numerical Simulation; Impeller; Cavitation; Specific Speed; Power

INTRODUCTION

Centrifugal pumps have been used in industrial and domestic applications such as steam power plants, water supply, sewage, drainage or irrigation plants, oil refineries, hydraulic power services and ships (^{Abo Elyamin et al., 2019}). Due to the value of the applications of these turbomachines, they have been subject of investigations aimed at improving their performance. (^{Domagała & Momeni, 2017}; ^{Lorusso et al., 2017}; ^{Al-Obaidi, 2019}; ^{Lai et al., 2019}; ^{Matlakala et al., 2019}; ^{Wang et al., 2019}; ^{Yousefi et al., 2019})

All these studies have been possible due to the development of high-performance computing means, which has allowed the evolution of a branch of fluid mechanics that through numerical methods such as Computational Fluid Dynamics (CFD), permits solving these physical phenomena in an approximate way to reality (^{Arias, 2020}).

In the above- mentioned investigations, the prototypes studied were virtual, this means that there was an anticipation of the operating results of these centrifugal pumps before manufacturing; that is, at the design stage. This confirms that the Computational Fluid Dynamics (CFD) method is a viable and adequate tool for conducting these investigations, due to its potential to accurately predict experimental results.

^{Moreno et al. (2018)}, carried out an investigation directed to determine the design parameters of a double suction centrifugal pump to transfer liquids (water and sugar cane juice), in the productive facilities of the sugar sector. With the results obtained it was possible to obtain 2D plans and 3D models, however, it is not possible to evaluate the performance of the pump once it is manufactured due to the lack of a test bank. Therefore, the present work is carried out and aimed to simulate, by means of the Computational Fluid Dynamics method, the performance of the double suction centrifugal pump BCP 125-420.

MATERIALS AND METHODS

Determination of the Ideal, Theoretical and Real Height

Equations 1, 2, 3 and 4 were used to determine the ideal, theoretical and real height. The input data were obtained from the results presented by ^{Moreno et al. (2018)}. The values of these parameters were necessary to be compared with the magnitudes predicted by simulation.

$H_{t\infty }=\frac{1}{g}(U_2\bullet V_{u2}-U_1\bullet V_{r1})$ , for a pump with radial inlet (1)

Where: $U_1$ - is the tangential velocity at the impeller inlet in m s^-1; $V_{u1}$ - is the input radial velocity in m s^-1; $U_2$ - is the peripheral velocity in m s^-1; $V_{u2}$ is the absolute exit velocity in m s^-1and g- is the acceleration of gravity in m s^-2.

To determine the theoretical height, expression 2 was used.

$H_{tz}=\mu \bullet H_{t\infty }$ (2)

Where: $\mu$ - is the correction coefficient by Stodola expression according to ^{Cherkasski (1986)} and $H_{t\infty }$ - is the ideal height in mwc.

$\mu =1-\frac{U_2}{V_{u2}}\bullet \frac{\pi }{Z}\bullet {sen\beta }_2$ (3)

Equation 4 was used to determine the real height of the pump.

$H_{bomba}={\mathrm{ɳ}}_h\bullet \mathrm{\mu }\bullet H_{t\infty }$ (4)

Where: ${\eta }_h$ - is the hydraulic performance, which, according to ^{Cherkasski (1986)} for modern centrifugal pumps, ranges between 0,8 and 0,96. For the case under study 0,9 was chosen.

Implementation of the Model in the Computational Tool

To develop this numerical analysis, the FluidFlow (CFX) calculation complement (Figure 1) was used, which belongs to ANSYS 14.5 software. By means of this complement it is possible to simulate the aerodynamics of vehicles such as automobiles or airplanes, combustion in engines, fluid in pumps and turbines; as well as studying heat transfer, analyzing chemical reactions, structural behavior caused by winds, hydraulic networks, circuit cooling, risks of fires and explosions.

FIGURE 1 FluidFlow calculation plug-in (CFX) 

The data used for pump simulation are represented in Table 1.

TABLE 1 Initial conditions for the simulation 

Initial Conditions	Value or description
Fluid Type	Water
Impeller speed	1750 min^-1
Inlet pressure	1 atm
Flow	0,041 m^3 s^-1
Fluid temperature	25ºC
Heat transfer	Isothermal

The boundary conditions for inlet and outlet are expressed as mass flow (converting to kg per second is sufficient).

Geometry

The three-dimensional bodies to be analyzed correspond to the volume of liquid contained in the pump: the suction pipe, the impeller, the casing and the discharge pipe. In the Geometry module, belonging to ANSYS, it is possible to generate geometries, although the methods are not very intuitive, so it was necessary to resort the importing of other CAD software.

The model corresponds to the fluid that occupies the interior of the pump, which is taken as the computational domain. Geometry is imported from SolidWorks design software in assembly form. The center of rotation of the impeller coincides with the x-axis (Figure 2).

FIGURE 2 Solid imported from SolidWorks. 

Consequently, the regions were declared. These are composed of one or more faces, where the boundary conditions are located (input, output and frequency of rotation), contact zones (suction, casing which is composed of suction and discharge, Figure 3 a and c, impeller and discharge) and the walls (Figure 3 b).

FIGURE 3 Statements of regions. a) Inlet wall. b) Impeller c) Discharge. 

These are the faces that are declared to locate the boundary conditions (walls, inlet, outlet and regions of rotation). Within the regions of rotation are the impeller blades and discs. The contact areas between bodies (casing outlet-impeller inlet and casing inlet impeller outlet)

As a total result for this model, 11 regions were generated: three in the suction, where the inlet condition, the wall and the contact zone with the housing liquid were located. Five regions were generated for the impeller: front disc, rear disc, blades, inlet and outlet. Three in the casing: inlet, outlet and wall. Finally, three at the discharge: inlet, outlet and wall (Figure 4).

FIGURE 4 Faces that are declared to locate the boundary conditions. 

Meshing

The quality of meshing is extremely important, since the precision of the results depends on it, as well as the computational time required by the software for the calculation does. Given that ANSYS Workbench software version 14.5 offers several possibilities, the automatic selection of the type of element, size (maximum and minimum), type of transition (fast or slow), types of smoothing at the edges and relevance, among others, were carried out. In this case, an automatic mesh was taken, adapted to the computational capabilities and the geometric complexity. The refinement of the mesh corresponds to the area of the cutter and the blades (Figure 5).

FIGURE 5 Mesh configuration for simulation. 

For the meshing of geometrically complex elements, as it is the case of the rotor (impeller) and the stator (volute) (Figure 6), an unstructured hexahedral mesh was used. As one of these elements rotates with respect to the other, it was necessary to establish a non-stationary mesh configuration that allows sliding (sliding mesh).

FIGURE 6 Meshing the model for simulation. 

In the case of inlet and outlet, a structured non-hexahedral mesh was used. In this way, it was generated a suitable number of elements, which allowed saving computational time without affecting the results (^{Caraballo et al., 2013}; ^{García et al., 2013}).

Settings for Pump Simulation

The atmospheric pressure was taken as a reference and, as the conservation of mass must be fulfilled, the inlet and outlet flows had to be the same. A subdomain was declared for the input casing, the impeller and another for the output casing (Figure 7).

FIGURE 7 Location of pump inlet and outlet conditions. 

In all the cases, it was taken into account that the fluid was water, at a temperature of 25 C (isothermal) and that it was a continuous medium. The turbulence model was k-Epsilon which showed a good relationship between the results and the computational consumption.

The casing walls were considered static (stator) as shown in Figure 8 (a) for rotating parts (rotor) at 1750 r.p.m. (Figure 8). For the direction of the rotation frequency, the x-axis was taken as a reference and the right-hand rule was applied.

FIGURE 8 Configuration. a) Computational domain of the volute. b) Computational domain of the runner. 

When analyzing the turbulence configuration, the configuration was the same for the case of the impeller and the volute (Figure 9).

FIGURE 9 Turbulence configuration for the computational domain. 

In order to find reliability in the simulation, it was established that the mean square root of the residuals (RMS) was 10^-4, as it can be observed in Figure 10.

FIGURE 10 Configuration for model reliability. 

Running the Calculation

To execute the calculation, it was necessary to specify, in the window provided by the software, some data that would depend on the features offered by the computer (Figure 11).

FIGURE 11 Computer configuration to run the model 

Method of Calculation of the Height Generated by the Pump

This height was determined by the mathematical Expression 1 ^{Chakraborty & Pandey (2011)} and was carried out in order to check if the height of the pump, once the simulation was carried out, agreed or was close to the desired one.

$H=\frac{P_{outlet-}{P}_{inlet}}{\rho \bullet g}$ (5)

Where: H- is the height generated by the pump; P outlet: is the pressure at the pump outlet, P inlet- is the pressure at the pump inlet, $\rho$ - is the density of water kg m^-3 and $g$ - is the acceleration of gravity in m s^-2.

Method for Determining the Error in Predictions

To determine the forecasting errors, the distance and error methods were used between the forecast (or modeled) values and the experimental results.

Errors were determined as:

$Error=\frac{V_{APD}-V_{PRE}}{V_{PRE}}\bullet 100$ (6)

Where: $V_{APD}$ - is the analytical value for the design and $V_{PRE}$ - is the predicted value by means of simulation.

Cavitation Coefficient Calculation Method

For the determination of this cavitation coefficient, the methodologies recommended by ^{Mataix (1986)} were followed. Where the values of the pressure at the inlet of the volute were taken as references for the calculation of this coefficient (^{Iannetti et al., 2016}), the saturation pressure of the steam (Pv) which for the case under study was water, the water density (ρ) and fluid velocity (V) as related by Equation 3.

$\sigma =\frac{P_s-P_v}{\mathrm{0,5}*\rho *v^2}$ (7)

RESULTS AND DISCUSSION

Results of Ideal, Theoretical and Real Pump Heights

The ideal height of the pump ( $H_{too})$ under study is 123,27 mwc; the theoretical height $\left(H_{tz}\right)$ for a certain number of blades (Z=5) is 90,973 mwc and the real height (Hpump) is 81,83 mwc. All the values obtained exceed the 80 mwc predicted by ^{Moreno et al. (2018)} for the determination of the design parameters.

Analysis of the Behavior of Velocities and Pressures

In order to determine the incidence of the geometric parameters on the operation of the double suction centrifugal pump, the values of the velocities and pressures at the inlet and outlet of the turbomachine were taken. In this way, it was possible to determine the height of the fluid generated by the pump. The distribution of the velocity values in the suction pipe is more homogeneous than in the discharge pipe because the fluid exiting the impeller at high velocities impacts the reed and changes direction abruptly and causes turbulence, recirculation, as shown in the graph of Figure 12 a.

FIGURE 12 Distributions in the pump of velocities a) and pressures b) 

In the case of pressures, it is evident that there is a marked difference in their values. Finding the smallest magnitudes in the center of the impeller, being greater in the periphery of it (Figure 12 b). This denotes that the principle of operation of the pump is fulfilled, where the kinetic energy of the fluid is converted into pressure energy.

The previous results agree with those reported by ^{Arias (2020)}; ^{Chakraborty & Pandey (2011)}; ^{Zhang et al. (2014)} regarding the principle of operation of a double suction centrifugal pump. The first ones of these authors carried out a numerical study on the effect of variations in the number of blades on the performance of a centrifugal pump at 4,000 r min^-1. The second ones carried out the optimization of the design of a double suction centrifugal pump using multi-objective optimization techniques and the subsequent simulation of the behavior of the pump by varying the shape of the impeller cover. And the third one optimized the operation of single suction radial centrifugal pumps, by varying geometric parameters using the response surface methodology and computational fluid dynamics. All these authors found these same trends regarding the behavior of velocities and pressures.

^{Zhang et al. (2014)}, however, reported that the pressure and velocities distributions are not symmetrical due to the volute, while both change periodically with the continuous rotation of the impeller.

These same parameters (speeds and pressures) are subsequently analyzed, but in the impeller of the pump under study. This verification is carried out in this machine element because ^{Mataix (1984)} refers that the exchange of mechanical energy between a fluid in a turbomachine is only verified in the impeller, since the remaining organs of the machine through which the fluid circulates are merely conduits or merely transformers of one form of energy, that the fluid already possesses, in another. Therefore, the energy exchange is verified in a mutual way (action and reaction) between the walls of the blades and the fluid.

The results of the parameters mentioned above (speed and pressure) can be observed in Figure 13. In the case of speeds, it is observed that their values in the fluid increase as the distance from the axis of the rotation towards the outer diameter of the impeller is greater (Figure 13 a). On the other hand, as a result of the action of the existing fiction between the surface of the impeller and the fluid, it is observed that the lowest velocity values are found in the walls of the impeller.

FIGURE 13 Distribution in the impeller of speeds a) and pressures b). 

In the case of pressure, the minimum values are found in the impeller's suction zone and the highest in the discharge zone, with magnitudes of 5,24 105 and 1,67 105Pa. As for the blades, the minimum values are in the convex zone and the highest in the concave zone (Figure 13 b). Overall, in terms of the trend of the results, they coincide with those reported by ^{Zhang et al. (2014)}; ^{Ding et al. (2019)} and ^{Arias (2020)}.

Analysis and Verification of the Height Generated by the Pump

Once the analysis of simulation of the pump operation was carried out, it was verified by means of Equation 1, that, when it is manufactured and put into operation, it will guarantee the value of the lifting height (H) for which it was designed. The results obtained from the prediction show a value of 81,65 mwc, magnitude that exceeds the expected 80 mwc, once the parameters for its design were determined by analytical calculations and that is close to the magnitude that the real height of the pump (H_pump) showed that is 81,87 mwc. It was obtained an error between the elevation height (H) predicted in the design stage and the elevation height predicted by simulation (Hpred) of 2,02%. On the other hand, the error between the lift height (H) predicted in the design stage and the lift height predicted by simulation (Hpred) was 2,28%. And the error between the actual pump height (Hbpump) and the elevation height predicted by simulation (Hpred) did not reach 1% with a value of 0,29%. These results indicate that the performance of the pump will be adequate once it is manufactured and put into operation.

Cavitation Coefficient Analysis

In centrifugal pumps, the phenomenon of cavitation deteriorates the impeller and blades, shortening their useful life and increasing maintenance and operating costs. To demonstrate the effectiveness of the proposed technique, test benches are used to generate cavitation by throttling the low-pressure valve that feeds the centrifugal pump, as is the case in the research carried out by ^{Albánez et al. (2016)}; although numerical methods such as Computational Fluid Dynamics (CFD) can also be used (^{Shojaeefard et al., 2012}; ^{Shah et al., 2013}).

To determine the cavitation behavior, the cavitation coefficient was used (σ), which yielded a value of 1.05, and it was determined by the data obtained through the simulation results.

When comparing the value of this coefficient, with that referred to by ^{Mataix (1986)}, it can be affirmed that the pump under study complies with the work and operation requirements of this type of pump (Figure 14). Because the magnitude of this coefficient (σ=1,05) and the specific speed (Ve=680) are within the permissible range for this type of pumps.

FIGURE 14 Coefficient of cavitation of the pump as a function of the specific speed. 1. Single intake pumps. 2. Double intake pumps. Source: ^{Mataix (1986)}. 

The validation of this result by means of the numerical method used indicates that the most prone zones to a phase change are the areas near the center of the impeller and the convex region of the blade (Figure 15).

FIGURE 15 Areas prone to cavitation. 

Result that agrees with those reported by ^{Ding et al. (2019)}, when investigating the influence of the blade exit angle on the performance of the centrifugal pump with high specific speed, as is the case of the double suction centrifugal pump BCP 125-420.

The previous results indicate that the operation of the double suction centrifugal pump under investigation will be adequate, where the effects of cavitation will be minimal.

Validation of Simulation Results

It is shown in Figures 16 and 17, that the law of conservation of mass, energy and momentum is fulfilled. The inlet and outlet flows were the same during the simulation of the operation of the double suction centrifugal pump, but with different signs. In addition, the difference in the conservation law between suction and discharge should not be greater than 1%.

FIGURE 16 Convergence of the residuals. 

FIGURE 17 Convergence of mass, energy, and motion. 

CONCLUSIONS

• The simulation of the performance of the BCP 125-420 double suction centrifugal pump in the ANSYS Workbench program allowed obtaining the values of the generated height and the cavitation coefficient, confirming that the operation of this machine will be adequate once it is manufactured. The values achieved were lifting height of 81.63 mwc and cavitation coefficient of 1,05.

• The magnitude of the error between the real height of the pump and that obtained through the simulation did not exceed 1%, a result that indicates the reliability of performance of the BCP 125-420 double suction centrifugal pump under the operation conditions studied.

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Received: September 18, 2020; Accepted: March 01, 2021

^*Author for correspondence: Alain Ariel de la Rosa-Andino, e-mail: [e-mail]

Ignacio David Moreno-Tamayo, Especialista, ASTIGOL, MINAL, Carretera Ciudad Pesquera, Código Postal 87510, Provincia Granma, Manzanillo, Cuba, e-mail: [e-mail]

Alain Ariel de la Rosa-Andino, Prof. Titular, Universidad de Granma, Facultad de Ciencias Técnicas, Dpto. de Ingeniería Mecánica, Carretera a Manzanillo, km 17 ½, Peralejo, Apartado 21, Bayamo, M. N. Código Postal 85149, Provincia Granma, Cuba, e-mail: [e-mail]

Yusimit Karina Zamora-Hernandez, Prof. Universidad Técnica Estatal de Quevedo, Facultad de Ciencias de la Ingeniería, Dpto. de Ingeniería Mecánica, Quevedo, Los Ríos, Ecuador, e-mail: Herná[e-mail]

Yoandrys Morales-Tamayo, Prof. Universidad Técnica de Cotopaxi, Facultad de Ciencias de la Ingeniería y Aplicadas, Dpto. Ingeniería Electromecánica, Extensión La Maná, Ecuador, e-mail: [e-mail]

René Misael Arias-Hidalgo, Prof. Instructor, Universidad de Granma, Facultad de Ciencias Técnicas, Dpto. de Ingeniería Mecánica, Carretera a Manzanillo, Provincia Granma, Cuba, e-mail: [e-mail]

Yordanka Aguilera-Corrales, Prof. Asistente, Universidad de Granma, Facultad de Humanidades, Manzanillo, Granma, Cuba, e-mail: [e-mail]

The authors of this work declare no conflict of interests.