Analysis of the influence of a stator type modification on the performance of a pump with a hole impeller

Abstract The article presents the results of numerical analyses and experimental research of the influence of various types of stators on a liquid flow through a centrifugal pump with a hole impeller. It is a continuation of authors research of cooperation pump stators with alternative types of impellers which work in ultra low specific speed. Hole impellers have become a significant alternative to classical ones in a range of extremely low specific speed nq<10. The aim of the research is to verify the quality as well as quantity of computer modeling results, and to estimate accuracy by examining the impact of a grid and a turbulence model with which the numerical simulations reflect the actual flow.Knowledge concerning construction of hydraulic elements of centrifugal pumps working in the range of parameters corresponding specific speed (nq<10) is insufficient. The outlet elements were tested in various configurations of constructional features. The complexity of the construction of the stator can significantly affect the manufacturing costs of pump unit.


Introduction
Pumps are the most commonly used among energy consuming decides in the industry. It is estimated that the transport of liquid in the economy absorbs 20-30% of energy production. Energy savings in pumping systems can be signi cant, there are estimates of the amount of possible energy savings in all areas of pump use at the level of 40% [1]. In many installations improper working conditions are imposed (for example too high pressure). In some systems, the pump units are old and work with low eciency. This forces a constant research for new construction of pumps parts -for example impellers or stators. It is necessary to increase the e ciency.
Wanting to improve the design of centrifugal pumpsespecially working in ultra low speci c speed -a better understanding of the ow phenomena of such machines is required. This paper discuss with the experimental and numerical study of the ow in the two types of pump stators -annular casing and spiral casing -which works with hole impeller. To a certain extent, it is a continuation of authors research [2] of cooperation pump stators with alternative types of impellers which work in ultra low speci c speed. Similar research have been performed in literature [3][4][5][6][7]. But in this studies have been used blade impellers in di erent types and con gurations. On the basis of these papers can be formulated fair conclusion, that the role of the geometry of outlet element becomes particularly important when considering innovational and unique constructions of the centrifugal rotor [8][9][10]. An good example of such a construction is a hole impeller which works in a range of ultra low speci c speed nq <10 (def. of nq according [1]), whose construction details were presented in Figure 1. It is a construction which uses a classical centrifugal liquid ow through the internal passages of the rotor to convert mechanical energy to hydraulic energy.
Due to a small outlet surface, located periodically along the circumference of the rotor, the construction of the stator cooperating with such a rotor is extremely demanding. To enhance conditions of that cooperation additional branch channels are sometimes applied in hole impellers (Figure 1b).
From a hydraulic point of view centrifugal pump consists of two, main elements: an impeller and the outlet element -stator. Rotor is responsible for converting mechanical energy of the electrical motor to hydraulic energy which is transferred to liquid. Pump stator collects liquid owing out of the rotor and carries it to the outlet ange of the pump (single stage pump) or to the inlet of the next stage impeller (multistage pumps). Also, it converts kinetic energy of the liquid -after the impeller outlet -into potential energy. The e ciency of this alteration strong determines performance of the whole pump. The last feature of pump stator: geometry of ow area a ects the BEP (Best E ciency Point) location on the pump ow characteristic. The outlet element is, therefore, a very crucial component, whose type and construction largely in uence pump's performance, the shape of ow characteristic, BEP location as well as e ciency level, as show the literature [2][3][4][5][6][7].
The aim of the following publication is to investigate the in uence of the type and construction of the stator, cooperating with a hole impeller with branch channels, on performance parameters and to recognize ow phenomena occurring in the pump using the earlier mentioned hydraulic elements. A volute type casing as well as an annular type casing at various con gurations of construction details of the mentioned elements were taken into consideration in the paper. The main research methodology were the CFD numerical analyses. Their results were experimentally veri ed on an appropriately built test rig.
An interesting conclusion has been discussed in the literature [1]. The authors claims that for centrifugal pumps with low and ultra low speci c speed it is better to apply a channel of a constant cross-section and simple geometry than an another stator -for example volute casing. As a main disadvantage of annular stator one can assume the fact that the streams of various speed are mixed, which in turn leads to higher hydraulic losses The di erence in e ciency between a annular channel and spiral casing diminishes, with the decrease of nq. The authors suggest that at speci c speed -nq <12 -the constant cross-section channel could represent higher e ciency than volute casing.This fact has been proved in the research presented in [2]. The results con rmed higher e ciency of centrifugal pump with multi-piped impeller in cooperation with an-nular casing. Also, in this article has been veri ed this interesting claim.

Object of research
A basic object of the experimental and numerical analysis is a hole impeller with branch channels, whose geometry and dimensions were presented in Figure 1c. The impeller consists of additional branch channels which -as was assumed -increase uniformity of velocity and pressure distribution in the stator. Therefore, they improve operating parameters. Geometric measurements of the impeller were shown in Figure 2a. A basic stator was an annular type casing. Dimensions were presented in Figure 2b. The outlet element was designed in a way which would allow a seamlessly exchange of pump ow parts.

Test rig
In order to verify the results of numerical calculations experimental tests on a test rig (Figure 3a) were planned and conducted. The main element of the test rig was a module, base pump ( Figure 3b). The following hydraulic components were applied for the test: a hole impeller and an annular-type casing, shown in Figure 2, later referred to as the base con guration. The test rig is so versatile that it is possible to examine various types of centrifugal impellers on it. Similar experimental tests have been performed in [2].
The measurements at the test rig were totally automated. The control software was customized for test rig in compliance with the European Standard [11]. More details concerning measuring instruments of the test rig as well methodology of measurements can be found in [2,12].

Numerical modeling
A fundamental research method applied in the project was the CFD (Computational Fluid Dynamics) [13]. Geometry of a stator and a hole impeller applied in the test rig module pump was created as a 3D model. Later, it referred to as the base con guration of liquid model of pump -named VB. Algorithm of numerical research was based on change type and geometrical parameters of stators cooperating with the impeller, however geometry of the rotor remained unaltered. Geometry of base con guration of annular casing was designed according to one dimension theory of vortex pump, included in literature [1].

. Numerical model
To determine and identify ow phenomena which take place during the ow in the pump with hole impeller with branch channels, for numerical CFD analyses Ansys Fluent from Ansys Workbanch 16.0 package was used. A simpli ed geometrical model of a base pump used for discretization was presented in Figure 5, and it consists of ow volumes: • The inlet element (the length of 4 diameters), • The impeller, • The annular-type casing, • The outlet element. The simulations were performed for the following settings: • Liquid -clean water of 20 • C, • double precision Solver, • calculation scheme: PISO algorithm [13][14][15][16], • for all equations the second order scheme discretization was assumed; • convergence criterion for each equation was ϵ = 10 − ; The CFD calculations were performed as transient, time step determined in accordance with [16] was ts = 5.2·10 − s. Rotational speed of the hole impeller was n = 2870 rpm (the speed of the electrical motor shaft). One rotation of an hole impeller has been divided at 120 time steps. Other boundary conditions were de ned compliant with Figure 5, as: • Inlet model -inlet velocity corresponding to given efciency of the pump, the intensity of turbulences at the inlet was determined T i = 4%. • Walls -zero pressure gradient dp/dn = 0, velocity ux = 0. • Outlet model -constant mass ow and liquid viscosity, static pressure corresponding roughly to the obtained head of the pump p = 300 kPa, intensity of reverse ow turbulence T ibf = 2%.

. Computational grid
To determine an optimal size of a grid The Grid Independence Test was performed. Calculations for four variants of grids were made, whose parameters were presented in Table 1. In each case, the tetrahedral type elements were used to discretization the grid. Boundary layer model was applied and concentrated in the areas of walls of the impeller and stator, which was shown in Figure 6. To Grid Independence Test k-ϵ Standard model was used. In order to expand the meaning of the headings used in Table 1 should be mentioned that: • The aspect ratio of an nite element in 3-D describes the proportional relationship between radius of circumscribed and inscribed circle at this element. • Skewness is one of the primary quality measures for a mesh. Skewness determines how close to ideal (i.e., equilateral or equiangular) a face or element is. • The Element Quality option provides a composite quality metric that ranges between 0 and 1. This metric is based on the ratio of the volume to the sum of the square root of the cube of the sum of the square of the edge lengths for 3D elements. A value of 1 indicates a perfect cube or square while a value of 0 indicates that the element has a zero or negative volume [15,16].
To assess the impact of the grid size on accuracy and time of calculations the following alterations of values were analyzed: moment on the blades (M t ) and the head (H), determined by the equation (1). The calculations results can be found in Figure 7.
While analyzing the results found in Figure 7 it can be noticed that the biggest di erence exists between the variants 1 and 2 (more than 23% for H and 6% for M t ). Between 2 and 3 the di erences in values do not exceed 13% for H and 2.9% for M t . However, the distinction in results between the grids 3 and 4 amounts to 2.7% for H and 0.8% for M t . For further calculations the computational grid corresponding variant 3 was assumed (element size was 0.125 mm for stator and 0.15 mm for impeller).

. Turbulence model
To choose an optimal turbulence model [15,16] for the discussed ow calculations for all two-equation turbulence models available in Fluent software were done. The calcu-  Table 2.
Convergence of the solution was attained for all available versions of the two-equation models. Model k-ω SST reached convergence criterion the fastest (after 683 iterations). The value of Hu and total e ciency ηc obtained during the experimental tests amounts to Hu = 21.8 and ηc = 31.5%. Obtained operating parameters for k-ω SST model were closest to experimental values. It can be inferred that the best accuracy was obtained for the turbulence model k-ω SST, which appears to be the best choice for the analyzed class of ows. In chosen model the y+ parameter on rotating surfaces does not exceed 1.

. Validation of numerical model
To evaluate accurateness of the assumptions for the CFD model of analyzed pump, the validation of results in the whole range of a pump characteristic was performed. The experimental test results and numerical calculations results was compared. Figure 8 shows a comparison of characteristics obtained on the test rig with the ones obtained numerically. While analyzing the results the following conclusions can be drawn: • In the whole area of a base pump -with a hole impeller and annular casing -the di erence between the numerical results and experimental ones does not exceed 6%. • For the ow rate corresponding BEP the di erence between the experimental test results and numerical ones does not exceed 1.1%. • For the ow rate higher than 6 m /h a drop of the ow characteristic can be noticed. That is likely to be a result of additional transient phenomena, such as cavitation, which were not modeled numerically. Similar ow characteristics were obtained in the work [13].

. Numerical study
The veri ed numerical model was applied in the tests on the in uence of the type and construction of the stator cooperating with a hole impeller with branch channels on the pump's ow rate.
Main energetic parameters of the tested pump were computed with the following equations: Total e ciency of the tested pump (4) was determined assuming constant values of volumetric e ciency ηv = 0.92 and mechanical e ciency ηm = 0.90 -in accordance with previously conducted research in [2,13] at the same test rig. The hydraulics e ciency is the key factor mainly for pumps working in nq < 10. Mechanical e ciency it depends on the losses in bearings and sealing (losses can be treated as constant value). Volumetric e ciency especially depends on the pressure di erence in an impeller gap sealing It is unchangeable value in tests, so the volumetric efciency can be treated as constant as well.

. Cooperation of a hole impeller with an annular-type casing
To analyze the cooperation of a hole impeller with an annular-type casing at various con gurations of construction features of the casing numerical calculations of the ow through the pump were performed. The following geometrical parameters of the annular type casing ware then changed ( Figure 9 Figure 15 one can notice that the decrease of the ow area caused the increase of velocity, nonetheless, the distribution of velocity in the channel is de nitely less uniform. • The base shape the channel cross-section (rectangular) appeared to be de nitively the best solution in comparison to the trapezoidal or semi-circular one - Table 3. That might be caused by the size of the cross-section area. Both the trapezoidal and semicircular channels signi cantly increase the surface area, which, as previous tests indicated, deteriorates energetic parameters of the pump. Moreover, in Figure 11 one can observe strong recirculation and turbulence in the cross-section of the channel. This is the result of a violent change of the direction of the liquid owing out of the rotor.  Figure 13) and static ( Figure 14) pressure as well as the distribution of velocity ( Figure 15). Reducing the outer diameter and the width (variant VM) of the channel resulted in the growth of velocity, nonetheless, velocity distribution in the channel is de nitely more uniform in comparison to VB - Figure 15. It a ects the decline hydraulic losses -lack of recirculation or turbulence areas. Furthermore, decreasing the outer diameter of the channel and its width (VM) a ected at the uniformity of total and static pressure distribution. In Figure 14 it can be observed that the increase of the static pressure is more uniform than in case of VB. Unfortunately, consequently, far greater decline of the static pressure appeared on the inlet edges to the ow channels of the impeller. Working conditions of an outlet di user were improved. It is used in a much higher degree. However, still water does not ow into it with the whole perimeter of the cross-section.

. Cooperation of a hole impeller with a volute type casing
In the next stage cooperation of a hole impeller with a spiral volute type casing at various con gurations of its geo-   Figure 16). • A change of a cross-section -rectangular, semicircular, trapezoidal.
The results of numerical calculations for the change of d and b kk were shown in Figure 17. In Table 4, however, one can nd the results for the change of the channel's pro le. Tests were performed for constant ow rate, cor-responding BEP (Q = 5.1 m /h). In Figure 17 a variant of maximum e ciency VM1 was marked with a vertical solid line, a dashed line, on the other hand, represents the base variant VB1. Geometry of primary volute casing was calculated and designed in accordance with theoretical models based on one-dimensional ow theory of vortex pump [1]. The constant and averaged velocity of liquid method was used (in the whole width of collector after impeller outlet).   • The alteration of the ow area relevantly in uences the improvement of ow parameters. In Figure 11 it is visible that the reduction of the ow area caused velocity increase, nevertheless, velocity distribution in the passage is de nitely more uniform. • As in the case of the annular type casing the results of a change of the cross-section shape did not improve pump's characteristic. The application of a semi-circular pro le in the volute casing also generates strong recirculation and turbulence in the channel's cross-section, narrowing the outlet from the impeller ( Figure 11). A slight increase of the ow area takes place in this case as well, which results in the decrease of ow parameters. The rectangular pro le, again, represents the best geometric features.
In Figure 18 characteristic of a pump with a hole impeller cooperating with a volute type casing VM1 can be found. Figure 19 - Figure 21 are graphic representations of the calculations results for the pump with an annular casing VB and a spiral type casing VM1, obtained for ow rate 5.1 m /h (BEP).
In the pictures the distribution of total ( Figure 19) and static pressure (Figure 20), and velocity distribution (Figure 21) were presented. As in the case of an annular type casing VM, a reduction of cross-sections in a volute type casing VM1 caused the increase of the liquid velocity while uniforming its distribution. Consequently, the zones of liquid recirculation and turbulence became eliminated -except for the area in the neighborhood of the volute tongue. In a volute type casing VM1 a more uniform distribution of static pressure was obtained ( Figure 20) than in case of anal annular type casing VM. This being due to the increase of the radius making the outline of the volute casing, thus, the channel becomes more regular and transforms ow energy much better.

Summary
The results of stator type modi cation in cooperation with hole impeller which is dedicated to work in ultra low speci c speed has been presented herein. Construction details of base and rationalized pump elements have been demonstrated as well as CFD and experimental test results. Hole impeller have become an important alternative to blade rotor in a range nq <10.
Summarizing the various stages of the above tests one can formulate the conclusions: • In the considered class of ow problem, the best turbulence model from the accuracy and calculation duration point of view is the model k-ω SST. • Calculation error of total e ciency and total head pump -obtained according to [17,18] -at pump capacity corresponding best e ciency point (BEP), did not exceed 2.6%. • It has been proven that a proper choice of the type and construction of the stator cooperating with a hole impeller can reduce turbulence and recirculation in the channel's cross-section. This a ects the improvement of the velocity distribution and total pressure. By proper selection of construction parameters like: outer diameter of a stator, width of an annular casing, width of volute casing and angle of volute tongue it is possible to improve e ciency (of nearly 14 percent point) and total head pump (over 20%) and a decrease in power demand by the pump (of almost 15%). • While discussing the cooperation results of a hole impeller with annular casing and spiral casing, it can be detected that the results obtained are almost comparable. This con rms the conclusion included in the literature [1,2]. It is reasonable to indicate that the annular casing is the best choice for cooperation with a hole impeller in the range of extremely low speci c speed nq <10. As a mainly advantages of annular stator are: simplicity of construction and low production costs. • Knowledge concerning construction of hydraulic elements of vortex pumps working is insu cient, especially if we move in range of extremely low speci c speed. As shown in the paper, the annular type casing VB cooperating with a hole impeller, designed in accordance with [1], reached far poorer operating parameters than the VM construction in a con guration with the same impeller.