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

  • Bartłomiej Chomiuk EMAIL logo and Janusz Skrzypacz
Published/Copyright: July 20, 2019
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Open Engineering
From the journal Open Engineering Volume 9 Issue 1

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.

Keywords: Low specific speed; centrifugal pump; hole impeller; stator type; CFD

1 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 significant, 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 efficiency. This forces a constant research for new construction of pumps parts – for example impellers or stators. It is necessary to increase the efficiency.

Wanting to improve the design of centrifugal pumps – especially working in ultra low specific speed – a better understanding of the flow phenomena of such machines is required. This paper discuss with the experimental and numerical study of the flow 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 specific speed. Similar research have been performed in literature [3, 4, 5, 6, 7]. But in this studies have been used blade impellers in different types and configurations. 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 specific 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 flow through the internal passages of the rotor to convert mechanical energy to hydraulic energy.

Figure 1 The hole impeller (a) top view, (b) basic hole impeller and (c) hole impeller with accessory additional branch channels
Figure 1

The hole impeller (a) top view, (b) basic hole impeller and (c) hole impeller with accessory additional branch channels

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 flowing out of the rotor and carries it to the outlet flange 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 efficiency of this alteration strong determines performance of the whole pump. The last feature of pump stator: geometry of flow area affects the BEP (Best Efficiency Point) location on the pump flow characteristic. The outlet element is, therefore, a very crucial component, whose type and construction largely influence pump’s performance, the shape of flow characteristic, BEP location as well as efficiency level, as show the literature [2, 3, 4, 5, 6, 7].

The aim of the following publication is to investigate the influence of the type and construction of the stator, cooperating with a hole impeller with branch channels, on performance parameters and to recognize flow phenomena occurring in the pump using the earlier mentioned hydraulic elements. A volute type casing as well as an annular type casing at various configurations 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 verified 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 specific 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 difference in effciency between a annular channel and spiral casing diminishes, with the decrease of nq. The authors suggest that at specific speed – nq<12 – the constant cross-section channel could represent higher effciency than volute casing.This fact has been proved in the research presented in [2]. The results confirmed higher effciency of centrifugal pump with multi-piped impeller in cooperation with annular casing. Also, in this article has been verified this interesting claim.

2 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 flow parts.

Figure 2 Dimensions of (a) basic hole impeller and (b) basic annular casing
Figure 2

Dimensions of (a) basic hole impeller and (b) basic annular casing

3 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 configuration. 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].

Figure 3 Presentation of test rig – (a) Test rig scheme and (b) the model pump without the front panel. Description of test rig scheme: 1 – tank, 2 – flowmeter, 3 – ball valve, 4,5 – pressure detectors, 6 – electric motor, 7 – flexible coupling, 8 – pump
Figure 3

Presentation of test rig – (a) Test rig scheme and (b) the model pump without the front panel. Description of test rig scheme: 1 – tank, 2 – flowmeter, 3 – ball valve, 4,5 – pressure detectors, 6 – electric motor, 7 – flexible coupling, 8 – pump

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].

The results of experimental tests of energetic characteristics of the module pump in the base form were shown in Figure 4. The Best Efficiency Point (BEP) of researched base pump with hole impeller is characterized by the following operating parameters:

Figure 4 Characteristics of the basic pump with an annular casing and a hole impeller
Figure 4

Characteristics of the basic pump with an annular casing and a hole impeller

  • capacity of pump Q = 5.1 m3/h (vst = 5.7 m/s, Re was about 62·103),

  • head pump Hu = 21.8 m,

  • total efficiency c = 31.5%.

This values will be used to build and verification a CFD model of pump with both stator types.

4 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 configuration 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 configuration of annular casing was designed according to one dimension theory of vortex pump, included in literature [1].

4.1 Numerical model

To determine and identify flow phenomena which take place during the flow in the pump with hole impeller with branch channels, for numerical CFD analyses Ansys Fluent from Ansys Workbanch 16.0 package was used. A simplified geometrical model of a base pump used for discretization was presented in Figure 5, and it consists of flow volumes:

Figure 5 Geometrical model of the pump with an annular casing and a hole impeller for numerical calculations
Figure 5

Geometrical model of the pump with an annular casing and a hole impeller for numerical calculations

  • 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 є = 10−6;

The CFD calculations were performed as transient, time step determined in accordance with [16] was ts = 5.2·10−4 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 defined compliant with Figure 5, as:

  • Inlet model – inlet velocity corresponding to given efficiency of the pump, the intensity of turbulences at the inlet was determined Ti = 4%.

  • Walls – zero pressure gradient dp/dn = 0, velocity ux = 0.

  • Outlet model – constant mass flow and liquid viscosity, static pressure corresponding roughly to the obtained head of the pump p = 300 kPa, intensity of reverse flow turbulence Tibf = 2%.

4.2 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 Figure6. To Grid Independence Test k-є Standard model was used.

Figure 6 Computational grid with close-up area of high elements concentration
Figure 6

Computational grid with close-up area of high elements concentration

Table 1

Properties of computational grids for each variant

VariantNumber of finite elementsSkewness (average)Aspect ratio (average)Element Quality (average)
16 754 5540.232.60.65
29 597 5160.222.180.67
314 192 3580.222.120.68
419 453 6740.222.060.74

In order to expand the meaning of the headings used in Table 1 should be mentioned that:

  • The aspect ratio of an finite 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 (Mt) and the head (H), determined by the equation (1). The calculations results can be found in Figure 7.

Figure 7 Influence of the grid size on the value of key computational parameters
Figure 7

Influence of the grid size on the value of key computational parameters

While analyzing the results found in Figure 7 it can be noticed that the biggest difference exists between the variants 1 and 2 (more than 23% for H and 6% for Mt). Between 2 and 3 the differences in values do not exceed 13% for H and 2.9% for Mt. However, the distinction in results between the grids 3 and 4 amounts to 2.7% for H and 0.8% for Mt. 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).

4.3 Turbulence model

To choose an optimal turbulence model [15, 16] for the discussed flow calculations for all two-equation turbulence models available in Fluent software were done. The calculations were performed for the computational grid variant 3 at a constant flow rate equal Q = 5.1m3/h. The results are shown in Table 2.

Table 2

Influence of the turbulence model

Lp.ModelConvergenceNumber of iterationsHuMtɳc
---mNm%
1k–ω StandardYES82321.282.56331.75
2k–ω SSTYES68321.562.56432.15
3k–є StandardYES68820.982.61430.69
4k–є RNGYES71221.112.58331.25
5k–є RealizableYES85621.022.62130.67

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 efficiency ɳc obtained during the experimental tests amounts to Hu = 21.8 and ɳc = 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 flows. In chosen model the y+ parameter on rotating surfaces does not exceed 1.

4.4 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:

Figure 8 Comparison of characteristics determined numerically and experimentally
Figure 8

Comparison of characteristics determined numerically and experimentally

  • In the whole area of a base pump – with a hole impeller and annular casing – the difference between the numerical results and experimental ones does not exceed 6%.

  • For the flow rate corresponding BEP the difference between the experimental test results and numerical ones does not exceed 1.1%.

  • For the flow rate higher than 6m3/h a drop of the flow characteristic can be noticed. That is likely to be a result of additional transient phenomena, such as cavitation, which were not modeled numerically. Similar flow characteristics were obtained in the work [13].

4.5 Numerical study

The verified numerical model was applied in the tests on the influence of the type and construction of the stator cooperating with a hole impeller with branch channels on the pump’s flow rate.

Main energetic parameters of the tested pump were computed with the following equations:

(1)Hu=pcout−pcinρg
(2)Pw=Mtω
(3)ηh=PhPw=ρgQHMtω
(4)ηc=ηhηvηm

Total efficiency of the tested pump (4) was determined assuming constant values of volumetric efficiency ɳv = 0.92 and mechanical efficiency ɳm = 0.90 – in accordance with previously conducted research in [2, 13] at the same test rig. The hydraulics efficiency is the key factor mainly for pumps working in nq< 10. Mechanical efficiency it depends on the losses in bearings and sealing (losses can be treated as constant value).Volumetric efficiency especially depends on the pressure difference in an impeller gap sealing It is unchangeable value in tests, so the volumetric efficiency can be treated as constant as well.

4.6 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 configurations of construction features of the casing numerical calculations of the flow through the pump were performed. The following geometrical parameters of the annular type casing ware then changed (Figure 9):

Figure 9 Basic dimensions of the annular type casing
Figure 9

Basic dimensions of the annular type casing

  • The outer diameter d4 of the channel - between 160 mm and 186 mm; base value 180 mm,

  • The width b3kk of the cross-section - between 16.5 mm and 26.5 mm; base value 22.5 mm,

  • The cross-section shape - rectangular, semi-circular, trapezoidal.

The results of the calculations can be found in Figure 10. Table 3, on the other hand, shows the results obtained after a change of the cross-section shape of a channel’s profile. The tests were performed for a constant flow rate, corresponding BEP (Q = 5.1 m3/h). A variant of maximum efficiency (VM)was marked with a vertical solid line, a base variant (VB) was marked with a dashed line.

Figure 10 Influence of alteration of the diameter d4 (a) and width b3kk (b) of the annular casing
Figure 10

Influence of alteration of the diameter d4 (a) and width b3kk (b) of the annular casing

Table 3

Influence of changes in the shape of the cross-sectional profile in the annular casing.

Lp.ProfileQMtHPhPwɳhɳc
-m3/hNmmWW%%
1rectangular profile5.12.37727.21377.2714.152.8544.22
2semi-circular profile5.12.68724.86344.9807.242.7335.75
3trapezoidal profile5.12.40126.54368.1720.951.0642.72

While analyzing the results of numerical calculations one can observe:

  • A reduction of the diameter d4 of 8% in relation to the base variant caused a relative increase of total efficiency of 9 percent point and the head of almost 17%, which resulted in a decline in power demand of more than 7%.

  • A decrease of the width of b3kk channel of nearly 18% in relation to the base variant caused a relative growth of total efficiency of about 4.6 percent point and a slight increase of the head – of 3.5%.

  • A change of geometry of the flow area had a essential influence on the betterment of flow parameters. The size of the flow area affects at direction and value of velocity vectors and pressure distribution of the liquid throughout the all over width of the annular casing. In Figure 15 one can notice that the decrease of the flow area caused the increase of velocity, nonetheless, the distribution of velocity in the channel is definitely less uniform.

Figure 11 Distribution of liquid velocity on the model lateral plan: (a) rectangular profie, (b) semi-circular profie and (c) trapezoidal profie
Figure 11

Distribution of liquid velocity on the model lateral plan: (a) rectangular profie, (b) semi-circular profie and (c) trapezoidal profie

Figure 12 Characteristics of the pump with a hole impeller and two types of annular casing – VB and VM
Figure 12

Characteristics of the pump with a hole impeller and two types of annular casing – VB and VM

Figure 13 Distribution of total pressure on the model central plane (a) base annular casing VB and (b) final annular casing VM
Figure 13

Distribution of total pressure on the model central plane (a) base annular casing VB and (b) final annular casing VM

Figure 14 Distribution of static pressure on the model central plane (a) base annular casing VB and (b) final annular casing VM
Figure 14

Distribution of static pressure on the model central plane (a) base annular casing VB and (b) final annular casing VM

Figure 15 Distribution of liquid velocity on the model central plane (a) base annular casing VB and (b) final annular casing VM
Figure 15

Distribution of liquid velocity on the model central plane (a) base annular casing VB and (b) final annular casing VM

  • The base shape the channel cross-section (rectangular) appeared to be definitively 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 significantly 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 flowing out of the rotor.

Figure 12 presents a comparison of characteristics of a pump with a hole impeller cooperating with the base annular type casing VB and VM. Figure 13 – Figure 15, on the other hand, show the results in a graphic form obtained for flow rate 5.1 m3/h (BEP). The pictures depict the distribution of total (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 definitely more uniform in comparison to VB – Figure 15. It affects the decline hydraulic losses – lack of recirculation or turbulence areas. Furthermore, decreasing the outer diameter of the channel and its width (VM) affected 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 flow channels of the impeller. Working conditions of an outlet diffuser were improved. It is used in a much higher degree. However, still water does not flow into it with the whole perimeter of the cross-section.

4.7 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 configurations of its geometric characteristic features was analyzed. The following parameters were tested (Figure 16):

Figure 16 Basic dimensions of a volute type casing
Figure 16

Basic dimensions of a volute type casing

  • The angle Bcw of the beginning of the volute tongue - between 0° and 26°; basic value 0°.

  • The width b3sp of the channel’s cross-section - between 10 mm and 20 mm; basic value 18.5 mm. For all CFD analyses the width of non-spiral part of volute casing was constant (value 18.5 in Figure 16).

  • A change of a cross-section - rectangular, semicircular, trapezoidal.

The results of numerical calculations for the change of d4 and b3kk were shown in Figure 17. In Table 4, however, one can find the results for the change of the channel’s profile. Tests were performed for constant flow rate, corresponding BEP (Q = 5.1 m3/h). In Figure 17 a variant of maximum efficiency 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 flow theory of vortex pump [1]. The constant and averaged velocity of liquid method was used (in the whole width of collector after impeller outlet).

Figure 17 Impact of changes of the angle Bcw location of a volute tongue (a) and the width b3sp (b) of the spiral casing
Figure 17

Impact of changes of the angle Bcw location of a volute tongue (a) and the width b3sp (b) of the spiral casing

Table 4

Influence of changes of the shape of the cross-sectional profile in a volute casing.

Lp.ProfileQMtHPhPwɳhɳc
-m3/hNmmWW%%
1rectangular profile5.12.52528.99402.1759.652.9344.28
2semi-circular profile5.12.66326.08369.5802.146.0638.53
3trapezoidal profile5.12.54328.28392.3768.251.0642.72

While analyzing the obtained results it can be noticed that:

  • The location of the beginning of the spiral volute, so called volute tongue is crucial in case of pumps working at low specific speed nq<10. The best solution appeared to be the angle 𝜷cw = 15°. Total efficiency was higher of 5 percent point in relation to other obtained values. Additionally, the head was over 20% higher.

  • Reducing the width of the volute casing b3sp in a slight degree impacted on the pump’s parameters. The increase of efficiency was insignificant and amounted to only 0.19 percent point. The head also grew not more than 0.2%. The decrease in power demand is practically negligible. An essential advantage of the change of the channel’s width is a question of enhancing the radius making the outline of the volute casing, thereby, the channel becomes more regular.

  • The alteration of the flow area relevantly influences the improvement of flow parameters. In Figure 11 it is visible that the reduction of the flow area caused velocity increase, nevertheless, velocity distribution in the passage is definitely 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 profile 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 flow area takes place in this case as well, which results in the decrease of flow parameters. The rectangular profile, 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 18 Characteristics of the pump with a hole impeller with an annular casing VB1 and a final volute casing VM1
Figure 18

Characteristics of the pump with a hole impeller with an annular casing VB1 and a final volute casing VM1

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 flow rate 5.1 m3/h (BEP).

Figure 19 Distribution of total pressure on the model central plane (a) base annular casing VB and (b) final volute casing VM1
Figure 19

Distribution of total pressure on the model central plane (a) base annular casing VB and (b) final volute casing VM1

Figure 20 Distribution of static pressure on the model central plane (a) base annular casing VB and (b) final volute casing VM1
Figure 20

Distribution of static pressure on the model central plane (a) base annular casing VB and (b) final volute casing VM1

Figure 21 Distribution of liquid velocity on the model central plane (a) base annular casing VB and (b) final volute casing VM1
Figure 21

Distribution of liquid velocity on the model central plane (a) base annular casing VB and (b) final volute casing VM1

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 a final 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 flow energy much better.

5 Summary

The results of stator type modification in cooperation with hole impeller which is dedicated to work in ultra low specific 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 flow problem, the best turbulence model from the accuracy and calculation duration point of view is the model k–ω SST.

  • Calculation error of total efficiency and total head pump – obtained according to [17, 18] – at pump capacity corresponding best efficiency 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 affects 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 efficiency (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 confirms 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 specific 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 insufficient, especially if we move in range of extremely low specific 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 configuration with the same impeller.

Nomenclature
b3

– width of a volute casing inlet [mm]

b3kk

– width of an annular casing [mm]

b3sp

– width of volute casing [mm]

d4

– outer diameter of a stator [mm]

g

– acceleration due to gravity [m/s2]

Hu

– total pump head [m]

Mt

– total moment on the impeller rotating surfaces [Nm]

n

– rotational speed [rpm]

nq

– kinematic specific speed (nq=nQ/Hu3/4)[rpm]

p

– ambient pressure [Pa]

pcin

– total pressure in an impeller inlet section [Pa]

pcout

– total pressure in a pump outlet section [Pa]

Ph

– hydraulic power [W]

Pw

– power on a pump shaft [W]

Q

– flow rate [m3/h]

Re

– Reynolds number,

ts

– time step [s]

ux

– velocity liquid in a perpendicular direction to the wall [m/s]

vst

– average uid velocity in stator [m/s]

βcw

– start angle of a spiral volute tongue [deg]

є

– convergence criterion

ɳc

– total efficiency

ɳh

– hydraulic efficiency

ɳm

– mechanical efficiency

ɳv

– volumetric efficiency

ρ

– density [kg/m3]

ω

– angular velocity [rad/s]

Acknowledgement

Calculations have been carried out using resources provided by Wroclaw Centre for Networking and Supercomputing (http://wcss.pl) grant No. 444/2017.

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Received: 2019-03-10
Accepted: 2019-05-27
Published Online: 2019-07-20

© 2019 Bartłomiej Chomiuk and Janusz Skrzypacz, published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/eng-2019-0029
Keywords for this article
Low specific speed; centrifugal pump; hole impeller; stator type; CFD
Creative Commons
BY 4.0

Articles in the same Issue

  1. Regular Article
  2. Exploring conditions and usefulness of UAVs in the BRAIN Massive Inspections Protocol
  3. A hybrid approach for solving multi-mode resource-constrained project scheduling problem in construction
  4. Identification of geodetic risk factors occurring at the construction project preparation stage
  5. Multicriteria comparative analysis of pillars strengthening of the historic building
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  12. Seasonal evaluation of surface water quality at the Tamanduá stream watershed (Aparecida de Goiânia, Goiás, Brazil) using the Water Quality Index
  13. EFQM model implementation in a Portuguese Higher Education Institution
  14. Assessment of direct and indirect effects of building developments on the environment
  15. Accelerated Aging of WPCs Based on Polypropylene and Plywood Production Residues
  16. Analysis of the Cost of a Building’s Life Cycle in a Probabilistic Approach
  17. Implementation of Web Services for Data Integration to Improve Performance in The Processing Loan Approval
  18. Rehabilitation of buildings as an alternative to sustainability in Brazilian constructions
  19. Synthesis Conditions for LPV Controller with Input Covariance Constraints
  20. Procurement management in construction: study of Czech municipalities
  21. Contractor’s bid pricing strategy: a model with correlation among competitors’ prices
  22. Control of construction projects using the Earned Value Method - case study
  23. Model supporting decisions on renovation and modernization of public utility buildings
  24. Cements with calcareous fly ash as component of low clinker eco-self compacting concrete
  25. Failure Analysis of Super Hard End Mill HSS-Co
  26. Simulation model for resource-constrained construction project
  27. Getting efficient choices in buildings by using Genetic Algorithms: Assessment & validation
  28. Analysis of renewable energy use in single-family housing
  29. Modeling of the harmonization method for executing a multi-unit construction project
  30. Effect of foam glass granules fillers modification of lime-sand products on their microstructure
  31. Volume Optimization of Solid Waste Landfill Using Voronoi Diagram Geometry
  32. Analysis of occupational accidents in the construction industry with regards to selected time parameters
  33. Bill of quantities and quantity survey of construction works of renovated buildings - case study
  34. Cooperation of the PTFE sealing ring with the steel ball of the valve subjected to durability test
  35. Analytical model assessing the effect of increased traffic flow intensities on the road administration, maintenance and lifetime
  36. Quartz bentonite sandmix in sand-lime products
  37. The Issue of a Transport Mode Choice from the Perspective of Enterprise Logistics
  38. Analysis of workplace injuries in Slovakian state forestry enterprises
  39. Research into Customer Preferences of Potential Buyers of Simple Wood-based Houses for the Purpose of Using the Target Costing
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  41. Hyperboloid offset surface in the architecture and construction industry
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  43. The selection of sealing technologies of the subsoil and hydrotechnical structures and quality assurance
  44. Impact of high temperature drying process on beech wood containing tension wood
  45. Prediction of Strength of Remixed Concrete by Application of Orthogonal Decomposition, Neural Analysis and Regression Analysis
  46. Modelling a production process using a Sankey diagram and Computerized Relative Allocation of Facilities Technique (CRAFT)
  47. The feasibility of using a low-cost depth camera for 3D scanning in mass customization
  48. Urban Water Infrastructure Asset Management Plan: Case Study
  49. Evaluation the effect of lime on the plastic and hardened properties of cement mortar and quantified using Vipulanandan model
  50. Uplift and Settlement Prediction Model of Marine Clay Soil e Integrated with Polyurethane Foam
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  52. A new method for graph stream summarization based on both the structure and concepts
  53. “Zhores” — Petaflops supercomputer for data-driven modeling, machine learning and artificial intelligence installed in Skolkovo Institute of Science and Technology
  54. Economic Disposal Quantity of Leftovers kept in storage: a Monte Carlo simulation method
  55. Computer technology of the thermal stress state and fatigue life analysis of turbine engine exhaust support frames
  56. Statistical model used to assessment the sulphate resistance of mortars with fly ashes
  57. Application of organization goal-oriented requirement engineering (OGORE) methods in erp-based company business processes
  58. Influence of Sand Size on Mechanical Properties of Fiber Reinforced Polymer Concrete
  59. Architecture For Automation System Metrics Collection, Visualization and Data Engineering – HAMK Sheet Metal Center Building Automation Case Study
  60. Optimization of shape memory alloy braces for concentrically braced steel braced frames
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  62. Feasibility Study of Microneedle Fabrication from a thin Nitinol Wire Using a CW Single-Mode Fiber Laser
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  65. Investigations of drilled and multi-piped impellers cavitation performance
  66. The novel solution of ball valve with replaceable orifice. Numerical and field tests
  67. The flow deteriorations in course of the partial load operation of the middle specific speed Francis turbine
  68. Numerical analysis of temperature distribution in a brush seal with thermo-regulating bimetal elements
  69. A new solution of the semi-metallic gasket increasing tightness level
  70. Design and analysis of the flange-bolted joint with respect to required tightness and strength
  71. Special Issue: Actual trends in logistics and industrial engineering
  72. Intelligent programming of robotic flange production by means of CAM programming
  73. Static testing evaluation of pipe conveyor belt for different tensioning forces
  74. Design of clamping structure for material flow monitor of pipe conveyors
  75. Risk Minimisation in Integrated Supply Chains
  76. Use of simulation model for measurement of MilkRun system performance
  77. A simulation model for the need for intra-plant transport operation planning by AGV
  78. Operative production planning utilising quantitative forecasting and Monte Carlo simulations
  79. Monitoring bulk material pressure on bottom of storage using DEM
  80. Calibration of Transducers and of a Coil Compression Spring Constant on the Testing Equipment Simulating the Process of a Pallet Positioning in a Rack Cell
  81. Design of evaluation tool used to improve the production process
  82. Planning of Optimal Capacity for the Middle-Sized Storage Using a Mathematical Model
  83. Experimental assessment of the static stiffness of machine parts and structures by changing the magnitude of the hysteresis as a function of loading
  84. The evaluation of the production of the shaped part using the workshop programming method on the two-spindle multi-axis CTX alpha 500 lathe
  85. Numerical Modeling of p-v-T Rheological Equation Coefficients for Polypropylene with Variable Chalk Content
  86. Current options in the life cycle assessment of additive manufacturing products
  87. Ideal mathematical model of shock compression and shock expansion
  88. Use of simulation by modelling of conveyor belt contact forces
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