- Email: [email protected]
The influence of micro grooves on the parameters of the centrifugal pump impeller
International Journal of Mechanical Sciences xxx (xxxx) xxx–xxx
Contents lists available at ScienceDirect
International Journal of Mechanical Sciences journal homepage: www.elsevier.com/locate/ijmecsci
The influence of micro grooves on the parameters of the centrifugal pump impeller ⁎
Janusz Skrzypacz , Marcin Bieganowski Wroclaw University of Technology, Faculty of Mechanical and Power Engineering, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland
A R T I C L E I N F O
A B S T R A C T
Keywords: Low specific speed CFD Micro-grooved impeller Rotodynamic pumps
Obtained efficiency of centrifugal pumps with low specific speed is not high. In order to reduce hydraulic losses, a modified impeller channel with micro grooves was designed and patented. The article focuses on the impact of microgeometry on the efficiency of centrifugal pumps with extremely low specific speed (nq < 8). The results of experiments carried out on a test rig were presented. The characteristics of centrifugal pumps with a smooth impeller and one with micro blades/micro grooves were compared. To identify the flow phenomena, preliminary CFD calculations were performed. The obtained distribution of pressure and velocity fields on specific control panels were compared.
1. Introduction The conception of micro grooves application (name proposed by the authors) was developed and patented [7] in the course of work on impellers of centrifugal pumps with extremely low specific speed. The idea includes the use of grooves inside the impeller passage, performed on the front and rear discs, which is presented in Fig. 1. This idea is based on three basic assumptions: 1. The increase of the influence of the impeller in the area of a boundary layer in the range of transmitting power to the liquid. In accordance with the one-dimensional flow theory a theoretical impeller consists of an infinite number of blades [1,3], therefore, each molecule of the liquid is moved in an individual inter-blade channel. In a real impeller (with a finite number of blades), the ability to transmit power to the liquid decreases, which measure is a slip factor [1,3]. The application of micro grooves should increase the ability of the impeller to transmit power to the liquid, particularly in the range of a boundary layer [9]. The main geometrical parameters of the impeller can be determined in accordance with one dimensional theory, presented in [1,8]. 2. The reduction of friction losses of rotating discs, which is carefully described in the patent [4]. 3. The protection against separation of the liquid at the diffuser flow. Impeller passages are diffusers whose maximum angle depends on the length of a channel and the area of cross sections: inlet and outlet. In the range of greater specific speed, when the passages become shorter and shorter and the sections of flow become bigger, ⁎
it may appear that the maximum angle of the diffuser becomes so big that the separation of the liquid from the channels’ walls might occur. One well-known method to protect the diffuser against that phenomena is the application of deflection grooves [2]. However, no information concerning such solution in terms of centrifugal pumps was found. To evaluate the conception of the application of microgeometry in centrifugal pumps’ impellers, the comparative experimental research of a smooth and micro-grooved impeller was carried out. Furthermore, preliminary CFD analyses were performed. Their aim was to identify the flow phenomena in the micro-grooved impeller. In order to obtain more complete material for analysis, the calculations of the flow through the ‘smooth’ impeller was carried out as well. To evaluate the conception of the application of microgeometry in centrifugal pumps’ impellers, the comparative experimental research of a smooth and micro-grooved impeller was carried out. Furthermore, preliminary CFD analyses were performed. Their aim was to identify the flow phenomena in the micro-grooved impeller. In order to obtain more complete material for analysis, the calculations of the flow through the ‘smooth’ impeller was carried out as well. 2. Objects of study Two impellers of identical geometry of the main flow system were used for experimental research. Though, one was smooth and the other was equipped in micro blades. Geometry of micro grooves was developed with the following assumptions:
Corresponding author. E-mail address: [email protected] (J. Skrzypacz).
http://dx.doi.org/10.1016/j.ijmecsci.2017.01.039 Received 20 September 2016; Received in revised form 18 January 2017; Accepted 20 January 2017 0020-7403/ © 2017 Elsevier Ltd. All rights reserved.
Please cite this article as: Skrzypacz, J., International Journal of Mechanical Sciences (2017), http://dx.doi.org/10.1016/j.ijmecsci.2017.01.039
International Journal of Mechanical Sciences xxx (xxxx) xxx–xxx
J. Skrzypacz, M. Bieganowski
Nomenclature d1 d2 H n
nq P Q β1 β2 η
inlet diameter [mm], diameter of the impeller [mm], total pump head [m], rotational speed [rpm],
kinematic specific speed [rpm], power on a pump shaft [W], flow rate [m3/h], inlet angle of the main passage [deg.], outlet angle of the main passage [deg.], total efficiency,
Fig. 1. Comparison of ‘smooth’ and micro-grooved impellers: a) smooth impeller, b) micro-grooved impeller – view from the shroud side, c) micro-grooved impeller – view from the hub side.
Fig. 2. A detail of grooves together with characteristic dimensions; a) detail of a groove; b) characteristic dimensions of a groove.
• In the cross section perpendicular to the shaft axis the shape of a groove is a pattern of the main blade outline. • The cross section of a groove is a rectangle, whose parameters were presented in Fig. 2. • The number of grooves in one impeller passage amounted to 10 (5
It has to be mentioned that in this stage of the project geometrical parameters of micro blades were chosen based on the authors’ experience and they were not optimized on the basis of the results of other studies. Details concerning typical geometrical features of impellers and their operation parameters were presented in Table 1.
on the impeller shroud, 5 on the impeller hub).
Table 1 Characteristic dimensions. Impeller variants Geometrical parameters Number of blades Diameter of the impeller d2, mm Inlet diameter d1, mm Diameter of the hub dp, mm Angle β1 Angle β2 Operating parameters (design point) Flow rate Q, m3/h Head m Rotational speed, rpm Micro geometry parameters Number of micro grooves Width of a micro groove, mm Depth of a micro groove, mm
1 - smooth
2 – with microblades
7 150 40 20 43 30 5,3 21,3 2950 – – –
70 0,5 0,1
Fig. 3. Test rig scheme: 1 – tank, 2 – flowmeter, 3 – ball valve, 4,5 – pressure detectors, 6 – electric motor, 7 – flexible coupling, 8 – pump.
2
International Journal of Mechanical Sciences xxx (xxxx) xxx–xxx
J. Skrzypacz, M. Bieganowski
Fig. 4. Graphic interface of the test rig.
3. The test rig
research of the impellers made in SLS technology were carried out on the test rig shown schematically in Fig. 3. Details concerning construction, equipment and accuracy of the test rig can be found in [6]. The process of the test is automatic, according to the procedure based on
In order to determine the influence of microgeometry on operation parameters as well as to check numerical calculations, experimental
Fig. 5. Head-discharge characteristics.
3
International Journal of Mechanical Sciences xxx (xxxx) xxx–xxx
J. Skrzypacz, M. Bieganowski
Fig. 6. Comparison of power consumption characteristics.
The characteristics of power consumption of the two studied impellers were presented in Fig. 6. In the range of efficiency from zero to that close to the BEP (best efficiency point) (ca. Q=6 m3/h), the impeller with micro grooves is characterized by comparable power consumption to the smooth one. After exceeding the BEP, the impeller with micro grooves consumes more power than the smooth one. It is visible in the chart that both characteristics of power consumption are not overloading.
[5]. The interface of the software steering the work of a computer was presented in Fig. 4, however, more details concerning the test rig can be found in [6]. 4. The results of experimental research Findings for the two studied impellers, in the form of pump carves, were presented in Figs. 5–7. When analyzing Fig. 5, which presents the comparison of flow characteristics of smooth and micro-grooved impellers, the following conclusions can be drawn:
5. Numerical calculations To determine and identify flow phenomena which take place during the flow in the micro-grooved impeller, thereby, to answer why the impeller with micro blades is characterized by a higher level of efficiency, numerical CFD analyses of the flow of the two studied impellers were performed. A simplified geometrical model of a pump used for discretization was presented in Fig. 8, and it consists of flow volumes:
1. In both cases characteristics are stable. 2. For the flow rate greater than 2 m3/h, the impeller with micro blades obtains much bigger head (for Q=6 m3/h the increase of h is of 17%, for Q=7.8 m3/h the increase of H is as much as 50%). 3. The impeller with micro grooves obtained a greater flow rate when the valve was fully open, which allows to assume that the presence of micro grooves increases capacity of the impeller.
Fig. 7. Comparison of efficiency characteristics.
4
International Journal of Mechanical Sciences xxx (xxxx) xxx–xxx
J. Skrzypacz, M. Bieganowski
Fig. 8. A simplified geometrical model of a pump.
1. 2. 3. 4.
The The The The
inlet element (the length of 4 diameters), Impeller, annular casing, outlet element. Fig. 9. Location of control planes.
Initial numerical calculations were performed for the constant rotational speed of the impellers n=2950 rot/min, according to the procedure presented in [6]. As a turbulence model the SST [1] model was initially used. Other significant boundary conditions were formulated as:
While analyzing the distribution of velocity vectors on given control planes it can be noticed that the closer to the boundary walls the better the liquid transportation. Micro grooves, through their interaction on the liquid, equalize velocity profiles between the adjacent current lines, which prevents the formation of reverse flows in the area of a boundary wall which, in turn, can influence the decrease of hydraulic losses. The comparison of the distribution of static pressure on particular control planes appears to be particularly interesting. The micro-grooved impeller is characterized by greater dynamic depression at the inlet to the inter-blade channel, which may probably result in poorer anticavitation properties in comparison to the smooth impeller. This aspect requires more thorough experimental research.
• INLET (Fig. 8) – inlet velocity corresponding to given efficiency of • •
the pump, the intensity of turbulences at the inlet was determined 5%, OUTLET (Fig. 8) – static pressure corresponding roughly to the obtained head of the pump (ca. 3,3 bar), LIQUID – pure water of 20 °C
5.1. Calculation results The results of calculations in a graphic form were presented in Fig. 10–76. Distributions of velocity and pressure were analyzed on three control planes: SPAN 10, SPAN 50, SPAN 90, for “smooth impeller” (SI) and micro-grooved impeller (MGI) which are presented in Fig. 9. While analyzing the distributions of velocity areas at different distance from the front disc, it can be noticed that the closer to the boundary wall of the impeller the more irregular (jaggy) the distribution of velocity in the micro-grooved impeller becomes in comparison to the areas of the smooth impeller. This being accompanied by better equalization of velocity in a given cross section. There are smaller differences of velocity between the adjacent areas, which prevents the formation of recirculating zones (there is no transport of energy through whirls between the surfaces). However, on the control plane located exactly in the middle of the width of the impeller's channel, it can be noticed that the distribution of velocity in both impellers is almost identical, which implies that the interaction of grooves becomes weaker with the distance from the boundary walls (Figs. 10–12).
6. Summary The use of microgeometry in the impellers of centrifugal pumps is an innovative, patented idea. Impellers with micro blades are characterized by more advantageous operating parameters in comparison to the smooth ones. On the basis of numerical calculations it can be concluded that the implementation of micro blades provides much better velocity distribution in an in impeller passages particularly in the area of passage walls, which results in the increase of the head and total efficiency of the pump. Further work is being performed in the following directions: 1. To check the influence of particular geometrical features of micro blades on operating parameters of the pump. 2. The assessment of the influence of micro blades on energetic parameters of pumps depending on the change of the pump specific speed.
5
International Journal of Mechanical Sciences xxx (xxxx) xxx–xxx
J. Skrzypacz, M. Bieganowski
Fig. 10. Comparison of velocity areas for one an impeller passage.
6
International Journal of Mechanical Sciences xxx (xxxx) xxx–xxx
J. Skrzypacz, M. Bieganowski
Fig. 11. The comparison of velocity vectors on control planes for one an impeller passage.
7
International Journal of Mechanical Sciences xxx (xxxx) xxx–xxx
J. Skrzypacz, M. Bieganowski
Fig. 12. Comparison of pressure distribution on control planes for one an impeller passage.
Warszawskiej, Warszawa; 2014. [4] Keizo Watanabe. Method for reducing disc friction by forming spiral groove, Patent JP2005233170 (A), Japan; 2005. [5] The European Standard EN ISO 9906. Rotodynamic pumps. Hydraulic performance, acceptance tests. Grades 1 and 2, BSI, 2003; 2000. [6] Skrzypacz J. Numerical modelling of flow phenomena in a pump with a multi-piped impeller. Chem Eng Process 2014;75:58–66. [7] Skrzypacz J. Wirnik pompy wirowej (Impeller of a rotodynamic pump), Patent PL381253, Poland; 2008.
References [1] Gulich J. Centrifugal Pumps. Berlin: Springer; 2008. [2] Jesionek KJ. Prognozowanie oderwania strumienia i możliwości jego ograniczania w przepływowych maszynach energetycznych (Forecasting of flow separation in turbomachinery – postdoctoral dissertation), Oficyna Wydawnicza Politechniki Wrocławskiej, Wrocław; 1998. [3] Jędral W. Pompy wirowe (Impeller pumps), Oficyna Wydawnicza Politechniki
8
International Journal of Mechanical Sciences xxx (xxxx) xxx–xxx
J. Skrzypacz, M. Bieganowski [8] Lei Tan, Baoshan Zhu, Shuliang Cao, Hao Bing, Yuming Wang. Direct and inverse iterative design method for centrifugal pump impellers; Influence of blade wrap angle on centrifugal pump performance by numerical and experimental study. Chin J
Mech Eng 2014;27(1). http://dx.doi.org/10.3901/CJME.2014.01.171. [9] Schlichting H, Gersten K. Boundary-Layer Theory. Berlin: Springer; 2017. http://dx. doi.org/10.1007/978-3-662-52919-5.
9
Contents lists available at ScienceDirect
International Journal of Mechanical Sciences journal homepage: www.elsevier.com/locate/ijmecsci
The influence of micro grooves on the parameters of the centrifugal pump impeller ⁎
Janusz Skrzypacz , Marcin Bieganowski Wroclaw University of Technology, Faculty of Mechanical and Power Engineering, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland
A R T I C L E I N F O
A B S T R A C T
Keywords: Low specific speed CFD Micro-grooved impeller Rotodynamic pumps
Obtained efficiency of centrifugal pumps with low specific speed is not high. In order to reduce hydraulic losses, a modified impeller channel with micro grooves was designed and patented. The article focuses on the impact of microgeometry on the efficiency of centrifugal pumps with extremely low specific speed (nq < 8). The results of experiments carried out on a test rig were presented. The characteristics of centrifugal pumps with a smooth impeller and one with micro blades/micro grooves were compared. To identify the flow phenomena, preliminary CFD calculations were performed. The obtained distribution of pressure and velocity fields on specific control panels were compared.
1. Introduction The conception of micro grooves application (name proposed by the authors) was developed and patented [7] in the course of work on impellers of centrifugal pumps with extremely low specific speed. The idea includes the use of grooves inside the impeller passage, performed on the front and rear discs, which is presented in Fig. 1. This idea is based on three basic assumptions: 1. The increase of the influence of the impeller in the area of a boundary layer in the range of transmitting power to the liquid. In accordance with the one-dimensional flow theory a theoretical impeller consists of an infinite number of blades [1,3], therefore, each molecule of the liquid is moved in an individual inter-blade channel. In a real impeller (with a finite number of blades), the ability to transmit power to the liquid decreases, which measure is a slip factor [1,3]. The application of micro grooves should increase the ability of the impeller to transmit power to the liquid, particularly in the range of a boundary layer [9]. The main geometrical parameters of the impeller can be determined in accordance with one dimensional theory, presented in [1,8]. 2. The reduction of friction losses of rotating discs, which is carefully described in the patent [4]. 3. The protection against separation of the liquid at the diffuser flow. Impeller passages are diffusers whose maximum angle depends on the length of a channel and the area of cross sections: inlet and outlet. In the range of greater specific speed, when the passages become shorter and shorter and the sections of flow become bigger, ⁎
it may appear that the maximum angle of the diffuser becomes so big that the separation of the liquid from the channels’ walls might occur. One well-known method to protect the diffuser against that phenomena is the application of deflection grooves [2]. However, no information concerning such solution in terms of centrifugal pumps was found. To evaluate the conception of the application of microgeometry in centrifugal pumps’ impellers, the comparative experimental research of a smooth and micro-grooved impeller was carried out. Furthermore, preliminary CFD analyses were performed. Their aim was to identify the flow phenomena in the micro-grooved impeller. In order to obtain more complete material for analysis, the calculations of the flow through the ‘smooth’ impeller was carried out as well. To evaluate the conception of the application of microgeometry in centrifugal pumps’ impellers, the comparative experimental research of a smooth and micro-grooved impeller was carried out. Furthermore, preliminary CFD analyses were performed. Their aim was to identify the flow phenomena in the micro-grooved impeller. In order to obtain more complete material for analysis, the calculations of the flow through the ‘smooth’ impeller was carried out as well. 2. Objects of study Two impellers of identical geometry of the main flow system were used for experimental research. Though, one was smooth and the other was equipped in micro blades. Geometry of micro grooves was developed with the following assumptions:
Corresponding author. E-mail address: [email protected] (J. Skrzypacz).
http://dx.doi.org/10.1016/j.ijmecsci.2017.01.039 Received 20 September 2016; Received in revised form 18 January 2017; Accepted 20 January 2017 0020-7403/ © 2017 Elsevier Ltd. All rights reserved.
Please cite this article as: Skrzypacz, J., International Journal of Mechanical Sciences (2017), http://dx.doi.org/10.1016/j.ijmecsci.2017.01.039
International Journal of Mechanical Sciences xxx (xxxx) xxx–xxx
J. Skrzypacz, M. Bieganowski
Nomenclature d1 d2 H n
nq P Q β1 β2 η
inlet diameter [mm], diameter of the impeller [mm], total pump head [m], rotational speed [rpm],
kinematic specific speed [rpm], power on a pump shaft [W], flow rate [m3/h], inlet angle of the main passage [deg.], outlet angle of the main passage [deg.], total efficiency,
Fig. 1. Comparison of ‘smooth’ and micro-grooved impellers: a) smooth impeller, b) micro-grooved impeller – view from the shroud side, c) micro-grooved impeller – view from the hub side.
Fig. 2. A detail of grooves together with characteristic dimensions; a) detail of a groove; b) characteristic dimensions of a groove.
• In the cross section perpendicular to the shaft axis the shape of a groove is a pattern of the main blade outline. • The cross section of a groove is a rectangle, whose parameters were presented in Fig. 2. • The number of grooves in one impeller passage amounted to 10 (5
It has to be mentioned that in this stage of the project geometrical parameters of micro blades were chosen based on the authors’ experience and they were not optimized on the basis of the results of other studies. Details concerning typical geometrical features of impellers and their operation parameters were presented in Table 1.
on the impeller shroud, 5 on the impeller hub).
Table 1 Characteristic dimensions. Impeller variants Geometrical parameters Number of blades Diameter of the impeller d2, mm Inlet diameter d1, mm Diameter of the hub dp, mm Angle β1 Angle β2 Operating parameters (design point) Flow rate Q, m3/h Head m Rotational speed, rpm Micro geometry parameters Number of micro grooves Width of a micro groove, mm Depth of a micro groove, mm
1 - smooth
2 – with microblades
7 150 40 20 43 30 5,3 21,3 2950 – – –
70 0,5 0,1
Fig. 3. Test rig scheme: 1 – tank, 2 – flowmeter, 3 – ball valve, 4,5 – pressure detectors, 6 – electric motor, 7 – flexible coupling, 8 – pump.
2
International Journal of Mechanical Sciences xxx (xxxx) xxx–xxx
J. Skrzypacz, M. Bieganowski
Fig. 4. Graphic interface of the test rig.
3. The test rig
research of the impellers made in SLS technology were carried out on the test rig shown schematically in Fig. 3. Details concerning construction, equipment and accuracy of the test rig can be found in [6]. The process of the test is automatic, according to the procedure based on
In order to determine the influence of microgeometry on operation parameters as well as to check numerical calculations, experimental
Fig. 5. Head-discharge characteristics.
3
International Journal of Mechanical Sciences xxx (xxxx) xxx–xxx
J. Skrzypacz, M. Bieganowski
Fig. 6. Comparison of power consumption characteristics.
The characteristics of power consumption of the two studied impellers were presented in Fig. 6. In the range of efficiency from zero to that close to the BEP (best efficiency point) (ca. Q=6 m3/h), the impeller with micro grooves is characterized by comparable power consumption to the smooth one. After exceeding the BEP, the impeller with micro grooves consumes more power than the smooth one. It is visible in the chart that both characteristics of power consumption are not overloading.
[5]. The interface of the software steering the work of a computer was presented in Fig. 4, however, more details concerning the test rig can be found in [6]. 4. The results of experimental research Findings for the two studied impellers, in the form of pump carves, were presented in Figs. 5–7. When analyzing Fig. 5, which presents the comparison of flow characteristics of smooth and micro-grooved impellers, the following conclusions can be drawn:
5. Numerical calculations To determine and identify flow phenomena which take place during the flow in the micro-grooved impeller, thereby, to answer why the impeller with micro blades is characterized by a higher level of efficiency, numerical CFD analyses of the flow of the two studied impellers were performed. A simplified geometrical model of a pump used for discretization was presented in Fig. 8, and it consists of flow volumes:
1. In both cases characteristics are stable. 2. For the flow rate greater than 2 m3/h, the impeller with micro blades obtains much bigger head (for Q=6 m3/h the increase of h is of 17%, for Q=7.8 m3/h the increase of H is as much as 50%). 3. The impeller with micro grooves obtained a greater flow rate when the valve was fully open, which allows to assume that the presence of micro grooves increases capacity of the impeller.
Fig. 7. Comparison of efficiency characteristics.
4
International Journal of Mechanical Sciences xxx (xxxx) xxx–xxx
J. Skrzypacz, M. Bieganowski
Fig. 8. A simplified geometrical model of a pump.
1. 2. 3. 4.
The The The The
inlet element (the length of 4 diameters), Impeller, annular casing, outlet element. Fig. 9. Location of control planes.
Initial numerical calculations were performed for the constant rotational speed of the impellers n=2950 rot/min, according to the procedure presented in [6]. As a turbulence model the SST [1] model was initially used. Other significant boundary conditions were formulated as:
While analyzing the distribution of velocity vectors on given control planes it can be noticed that the closer to the boundary walls the better the liquid transportation. Micro grooves, through their interaction on the liquid, equalize velocity profiles between the adjacent current lines, which prevents the formation of reverse flows in the area of a boundary wall which, in turn, can influence the decrease of hydraulic losses. The comparison of the distribution of static pressure on particular control planes appears to be particularly interesting. The micro-grooved impeller is characterized by greater dynamic depression at the inlet to the inter-blade channel, which may probably result in poorer anticavitation properties in comparison to the smooth impeller. This aspect requires more thorough experimental research.
• INLET (Fig. 8) – inlet velocity corresponding to given efficiency of • •
the pump, the intensity of turbulences at the inlet was determined 5%, OUTLET (Fig. 8) – static pressure corresponding roughly to the obtained head of the pump (ca. 3,3 bar), LIQUID – pure water of 20 °C
5.1. Calculation results The results of calculations in a graphic form were presented in Fig. 10–76. Distributions of velocity and pressure were analyzed on three control planes: SPAN 10, SPAN 50, SPAN 90, for “smooth impeller” (SI) and micro-grooved impeller (MGI) which are presented in Fig. 9. While analyzing the distributions of velocity areas at different distance from the front disc, it can be noticed that the closer to the boundary wall of the impeller the more irregular (jaggy) the distribution of velocity in the micro-grooved impeller becomes in comparison to the areas of the smooth impeller. This being accompanied by better equalization of velocity in a given cross section. There are smaller differences of velocity between the adjacent areas, which prevents the formation of recirculating zones (there is no transport of energy through whirls between the surfaces). However, on the control plane located exactly in the middle of the width of the impeller's channel, it can be noticed that the distribution of velocity in both impellers is almost identical, which implies that the interaction of grooves becomes weaker with the distance from the boundary walls (Figs. 10–12).
6. Summary The use of microgeometry in the impellers of centrifugal pumps is an innovative, patented idea. Impellers with micro blades are characterized by more advantageous operating parameters in comparison to the smooth ones. On the basis of numerical calculations it can be concluded that the implementation of micro blades provides much better velocity distribution in an in impeller passages particularly in the area of passage walls, which results in the increase of the head and total efficiency of the pump. Further work is being performed in the following directions: 1. To check the influence of particular geometrical features of micro blades on operating parameters of the pump. 2. The assessment of the influence of micro blades on energetic parameters of pumps depending on the change of the pump specific speed.
5
International Journal of Mechanical Sciences xxx (xxxx) xxx–xxx
J. Skrzypacz, M. Bieganowski
Fig. 10. Comparison of velocity areas for one an impeller passage.
6
International Journal of Mechanical Sciences xxx (xxxx) xxx–xxx
J. Skrzypacz, M. Bieganowski
Fig. 11. The comparison of velocity vectors on control planes for one an impeller passage.
7
International Journal of Mechanical Sciences xxx (xxxx) xxx–xxx
J. Skrzypacz, M. Bieganowski
Fig. 12. Comparison of pressure distribution on control planes for one an impeller passage.
Warszawskiej, Warszawa; 2014. [4] Keizo Watanabe. Method for reducing disc friction by forming spiral groove, Patent JP2005233170 (A), Japan; 2005. [5] The European Standard EN ISO 9906. Rotodynamic pumps. Hydraulic performance, acceptance tests. Grades 1 and 2, BSI, 2003; 2000. [6] Skrzypacz J. Numerical modelling of flow phenomena in a pump with a multi-piped impeller. Chem Eng Process 2014;75:58–66. [7] Skrzypacz J. Wirnik pompy wirowej (Impeller of a rotodynamic pump), Patent PL381253, Poland; 2008.
References [1] Gulich J. Centrifugal Pumps. Berlin: Springer; 2008. [2] Jesionek KJ. Prognozowanie oderwania strumienia i możliwości jego ograniczania w przepływowych maszynach energetycznych (Forecasting of flow separation in turbomachinery – postdoctoral dissertation), Oficyna Wydawnicza Politechniki Wrocławskiej, Wrocław; 1998. [3] Jędral W. Pompy wirowe (Impeller pumps), Oficyna Wydawnicza Politechniki
8
International Journal of Mechanical Sciences xxx (xxxx) xxx–xxx
J. Skrzypacz, M. Bieganowski [8] Lei Tan, Baoshan Zhu, Shuliang Cao, Hao Bing, Yuming Wang. Direct and inverse iterative design method for centrifugal pump impellers; Influence of blade wrap angle on centrifugal pump performance by numerical and experimental study. Chin J
Mech Eng 2014;27(1). http://dx.doi.org/10.3901/CJME.2014.01.171. [9] Schlichting H, Gersten K. Boundary-Layer Theory. Berlin: Springer; 2017. http://dx. doi.org/10.1007/978-3-662-52919-5.
9