Energy efficiency analysis of double suction centrifugal pumps with new impeller geometry

. The development of energy saving determines the importance of improving the efficiency of equipment that uses most of the energy consumed. Pumping equipment is one of the most significant consumers of electrical energy. Thus, the drive of pumps (mainly centrifugal pumps) at some CHPPs consumes up to 10 % of the total energy produced at the plant [1]. In general, the total share of consumption of pumping equipment operated in industry, according to various estimates, is from 15 to 25 % of all generated electricity. In this paper, a new impeller configuration (with variable blade curvature) for double suction centrifugal pumps with higher efficiency was proposed. The head and efficiency of centrifugal pump with different vane grids were compared. The main conclusions are that the static pressure and relative velocity have increased in the modernised impeller, leading to an increase in hydraulic and overall efficiency, the kinetic energy of turbulence has less pulsation. the operating point of the pump has shifted. In spite of the fact that the average integral efficiency has increased in the modified pump, the operating point of the pump is shifted to the side of decreasing flow by 1.5%. The theory of the variable curvature vane system was verified by computational methods.


Introduction
There are currently two main ways of solving the problem of improving the efficiency of pumping equipment: the design and manufacture of new pumps, more advanced than the previous generation, or the modernisation of existing equipment.The second waymodernisation of existing pumps -provides an opportunity for a relatively quick and low-cost set of measures to increase the efficiency and reliability of pumping equipment When analysing and researching the most promising methods, we have identified directions for improving the flow part of the impeller.So in the work [2] studied the influence of impeller angles of double suction, it was found that, changing the angles of blade inclination can cause pressure fluctuations with high amplitude vibration of centrifugal pumps with double suction The authors conducted experiments on pressure fluctuations are conducted for five configurations of impeller with different angles of inclination using the same test bench system.The results show that the offset angles have a negligible effect on the head characteristics and efficiency.The inclination angle has a minor effect on the pressure fluctuations in the suction chamber, while it has a major effect on the pressure fluctuations in the volute casing, especially in the aspect of decreasing amplitude at the blade pass frequency.
In the direction of increasing the efficiency by modernising the vane system, the author [3] proposes a centrifugal pump impeller which contains at least two vanes with different entry angle βl1.All impeller blades are arranged with a constant external pitch α and have the same exit angle βl2.In a particular case, each impeller blade corresponds to a blade with the same entry angle βl1 arranged symmetrically ab out the centre of the impeller.The impeller may include three pairs of blades with different entry angles βl1.The efficiency of the pump is increased in the area of flow values different from the design value.
One of the possible directions for solving the problem of increasing the efficiency and energy efficiency of CNs is the idea of using double-deck RCs, which has attracted the attention of researchers both in the field of pump engineering [4][5][6][7].The application of wheels with double-deck grating was firstly suggested by Pfleiderer.He points out the possibility of using a wheel of this design when the outlet constriction factor is significant.The first practical attempts to implement and test this idea in order to increase the efficiency of the stage and improve the shape of the pressure characteristic did not lead to the expected result.
The authors of the work suggest replacing the spatial vane system of the centrifugal impeller with a low (ns = 65) specific speed of rotation with cylindrical blades, because such working bodies most intensively carry out the process of energy transfer from the impeller to the working fluid.This will provide an increase in the impeller head and simplification of its manufacturing technology.[8]

Basic Parameters of the Impeller
The two main components of a centrifugal pump are the impeller and the casing.The other components are the suction nozzle, discharge nozzle, shaft, bearing, wear rings, stuffing box and mechanical seal.
A double suction impeller is essentially no different from two single suction impellers, arranged closely together on a horizontal shaft and supported by supports on both sides.This design allows for increased capacity without increasing the impeller diameter.This type allows the fluid to enter the impeller eyelet on both sides.This action can be symmetrical about the centre line of the double suction impeller.The symmetry of the impeller greatly improves its hydraulic balance or no axial thrust force.The centre helix serves both impellers and leads through one diffuser to the outlet flange [9].This arrangement often results in higher efficiency because it reduces the friction at the back of the impellers, the friction losses of the discs, and because the specific speed of each impeller is sometimes greater when the flower is split in two.favourable.As a result, double suction volute pumps can generate higher pressures than single suction centrifugal pumps [10].
The The method of industrial tests for determining the efficiency of the pump consists in determining the pressure and energy characteristics of the pump at five points in the working range of the pump, which is usually a flow rate from 0.5 QH to 1.5 QH.The delivery is regulated by an automatic gate valve.In the figure 2 To conduct a numerical study of the flow structure in the flowing part of the RC for various methods of head increase using the licensed software product CRADLE/Sflow university version.This software product is based on the method of numerical solution of the fundamental laws of hydromechanics [11] of the equations of motion of a viscous fluid together with the continuity equation.This is a sufficient condition for the validity of the application of the results of the numerical study.The flow was calculated by numerical solution of the system of equations describing the most general case of fluid medium motion -the Navier-Stokes equations (1) and the continuity equation ( 2) [12].The equations are presented in the reduced form (i, j = 1-3), summation by the same indices is assumed ( ) ( ) where xi, xj -are coordinate axes; fi -component expressing the action of mass forces As boundary conditions, the condition of "sticking" on solid walls (velocity equals zero), distribution of all velocity components in the inlet section, and equality to zero of the first derivatives (in the direction of flow) of the velocity components in the initial section are set For closure of the Reynolds equations in CRADLE/Sflow, a number of turbulence models are used.A complete list of the capabilities of this software product, its mathematical apparatus and basic hydrodynamics models can be found in the documentation for this software product The SST turbulence model is best suited for such calculations, and several problems have been calculated using k-g and k-y turbulence models.All of these turbulence models support the method of near-wall functions, which relate the flow parameters to the distance from the wall.This avoids the use of very fine meshes near the wall.The flow was calculated in a stationary formulation.The working medium (water under normal conditions) was assumed to be incompressible and the flow regime was assumed to be turbulent [13].
The following assumptions were made during the numerical study: -the flow at the inlet to the design region is axisymmetric; -there is no influence of leakage through the RK seals on the flow in the flow section

Method to Modify the Impeller
The concept of variable pitch (Figure 3) is based on the ideas of redistributing predominantly impact losses at the inlet of the impeller blade system throughout the impeller.
The realisation of such solutions implies the use of new design approaches.In particular, the vane system of the pump is calculated not for one point (Qacc,Hacc), but for the required flow area (Q(Q1, Q2...Qn), H(H1, H2...Hn)).
Thus formed hydrodynamic grid has different angles of inclination and width of channels.As a consequence, the working area of the pump is widened.Thus the average integral efficiency of the pump with heterogeneous vane system is higher than that of analogues with classical (homogeneous) vane system.Shock losses in the pump wheel are determined according to the method [14,15] According to for the projections of absolute velocities on the circumferential direction on the angle of flow and the circumferential direction on the structural angle of the blade we write down: -projection of absolute velocity on the circumferential direction by the flow angle: ( where: ℎ sh.н − flow loss on shock at the entrance to the wheel;  н --impact loss coefficient of the impeller grille ∆ н1 2difference of circumferential components of absolute velocity at deviations of flow direction from its direction in the shockless entry mode.
For the projections of absolute velocities on the circumferential direction by the flow angle and the circumferential direction by the blade design angle we write: -absolute velocity projection on the circumferential direction along the flow angle: where:  1нcircumferential speed;  1нflow angle on the blade;  н1 -wheel entry radius;  н1inlet wheel channel width;  1н -flow restriction factor; -projection of the absolute velocity onto the circumferential direction along the grating angle: where:  1н -angle of the flow on the blade along the grate angle At a flow rate corresponding to a shockless entry to the wheel, the difference in the circumferential velocity components at the entrance to the NC: where: We have: Given the ratio )  0 (11)

Then it's easy to get:
The method of construction of different blades for the modified wheel was as follows, according to the data of the range of variation of the feed, according to industrial tests, the heads and geometrical parameters of three blades of the heterogeneous grid were determined from the Q-H characteristics curve (Figure 3), Figure 4 shows the programme windows with the coordinates of the blades.

Mesh generation
The computational meshes were created using the ICEM CFD mesh generator for their construction.It allows for forced adjustment of the mesh density, densifying it in necessary places (e.g. at the blade inlet and outlet edges) and enlarging it where high mesh density is not required.This approach allows saving computer resources and obtaining sufficient grid density in the investigated part of the computational domain.Before conducting the study, a grid independence check was performed.For this purpose meshes with different densities were constructed.[16] Figure 5 shows the stages of mesh generation.

Fig. 5. Mesh generation stages.
The impeller sub-area was covered with a uniform unstructured mesh of tetrahedral cells, and the outlet sub-area with a regular hexagonal mesh Figure 7. Mesh adaptation was not performed because, firstly, the use of standard wall functions does not require too fine a mesh ( min + y = 30 ÷ 60), and secondly, the lack of computational resources prevented further improvement of the solution.Computational meshes with 600 thousand, 800 thousand and 1mn cells were constructed.The analysis of integral values obtained from the numerical results for meshes with different densities showed that the results differ by no more than 1 % when the number of cells exceeds 700 thousand.This result indicates the mesh independence.Further numerical study was carried out for meshes having ≈ 700 thousand cells.The value of the variable y+ , which characterises the densification of the mesh near the walls, was in the range 20< y+ <60 units, [17].Boundary conditions were set on the wheel wall -Wall: zero tangential velocity (condition of "sticking" to the wall), zero velocity of the wall itself relative to the rotating coordinate system (i.e., the wall moves synchronously with it).On the outlet wall -Wall: zero tangential velocity (condition of "sticking" to the wall), zero velocity of the wall itself relative to the absolute inertial coordinate system (i.e. the wall is stationary).

Verification of the algorithm
The above algorithm is used for numerical simulation The above algorithm is used for numerical simulation of the internal flow of the original centrifugal pump and the optimised centrifugal pump.To check the validity of the algorithm used, calculations were carried out for the working area of the pump according to the experimental data in Figure 6  The results of the pressure characteristics of the pump, obtained by calculations in CRADLE/Sflow software and the experimental results from the factory, were summarised in the comparison diagram shown in Figure 7.
Analysing the integral characteristics obtained on the experimental bench and comparing them with the results of numerical simulation (Figures 8,9), we can conclude that the discrepancy between the results for head is about 4%.Analysing the fact of mismatch of characteristics, it can be assumed that the most probable reason for this behaviour of curves is the discrepancy between the geometrical model of the vane systems used in calculations and those actually manufactured.In particular, it concerns the shape of the inlet and outlet edges, the roughness of the flow part, etc. as well as the error of physical measurements, but the difference is quite acceptable, which confirms the adequacy of the computer model of the wheel.

Numerical Simulation Results
To measure the effect of variable curvature vanes on the performance of a centrifugal pump, the changes in static pressure, relative velocity and turbulence kinetic energy in the middle part of the impeller were analysed under typical flow conditions (low flow rate 0.5 Q and 0. According to the modelling results, the general law of static pressure variation is that the static pressure in the different channels of the wheel is distributed uniformly.The static pressure drops for the original wheel are 0.36MPa to 0.528MPa and for the wheel with blades of variable curvature from 0.44MPa to 0.63MPa at all investigated feed modes.as shown in Figure 11.The static pressure was lowest at the inlet of the impeller.The static pressure at the impeller outlet was the highest.For all impellers, the static pressure generally increased with increasing flow rate.Under the condition of 0.7 Q, the increase in static pressure was more pronounced.At the outlet, the static pressure reached the maximum value at condition 1.5 Q. Visualisation of the pressure distribution gradient shows a decrease in the underpressure zones in the modified wheel, i.e. a decrease in the occurrence of reverse currents in the wheel with heterogeneous lattice.The volume of the distribution gradually decreased as the flow velocity increased.
Velocity diagrams allowed us to observe the increase of relative velocity in the modernised wheel, so at minimum feed rate the velocity in the original wheel is 45m/s in the modernised wheel 47m/s and at maximum feed rate 56m/s for the original wheel and 59m/s for the modernised wheel, the increase of relative velocity will affect the hydraulic efficiency.
The distribution diagram of turbulent kinetic energy at low flow velocity in the original wheel has a large surface coloured blue, which indicates a higher value of turbulence and behind the wheel are seen pronounced red areas of maximum values of vortices, which naturally leads to a decrease in efficiency in this mode of operation of the pump.Whereas in the modified wheel all areas of turbulence are coloured blue, and only locally appear vortices.Pump losses at low flow rates are higher in the similar impeller.
According to the results of efficiency and pressure characteristics obtained by the method of computational fluid dynamics in CRADLE system, graphs were plotted (Figure 10).In the diagrams, the intersection of the Q-H curve and the efficiency curves, which were plotted according to the results of calculations, correspond to the operating points of the pump.Obviously, despite the fact that the efficiency in the modified pump has decreased at rated flow, the operating point and the average integral efficiency has increased by 2%, but the operating point has shifted towards a decrease in flow by 1.5%.

Conclusions
In this paper, the effect of retrofitting the vane system of a centrifugal pump wheel on the pressure-energy characteristics was investigated.Numerical simulations of flows in a centrifugal pump with homogeneous and heterogeneous vane wheels were carried out at low flow, nominal flow and high flow.
Changes in static pressure, relative velocity, and turbulence kinetic energy were analysed.
The theory of the variable curvature vane system was verified by computational methods.
The head and efficiency of a centrifugal pump with different vane arrays were compared.
The main conclusions are that the static pressure and relative velocity have increased in the modernised wheel, leading to an increase in hydraulic and overall efficiency, the kinetic energy of turbulence has less pulsation.the operating point of the pump has shifted.In spite of the fact that the average integral efficiency has increased in the modified pump, the operating point of the pump is shifted towards a decrease in flow by 1.5%.The theory of the vane system with variable curvature has been verified by computational methods.

Fig. 6 .
Fig. 6.Modelling results a) pressure distribution in the wheel b) file with results.

Fig. 8 . 6 MATECFig. 9 .
Fig. 8. Results of simulation of flow kinematics in a wheel with a homogeneous grid.

Fig. 10 .
Fig. 10.Pressure and energy characteristics of the pump (a) for the pump with the original impeller (b) for the pump with the modified impeller.

Table 1 .
Technical characteristics of the pump and geometrical characteristics of the impeller.