INVESTIGATION OF FLOW INSIDE AN AXIAL-FLOW PUMP OF GV IMP TYPE

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1 1 INVESTIGATION OF FLOW INSIDE AN AXIAL-FLOW PUMP OF GV IMP TYPE ANATOLIY A. YEVTUSHENKO 1, ALEXEY N. KOCHEVSKY 1, NATALYA A. FEDOTOVA 1, ALEXANDER Y. SCHELYAEV 2, VLADIMIR N. KONSHIN 2 1 Depatment of Applied Fluid Mechanics, Sumy State Univesity, Rimsky-Kosakov st., 2, 40007, Sumy, Ukaine 2 OOO TESIS, Office , Unnatov st., 18, , Moscow, Russia Abstact: The aticle descibes eseach of fluid flow inside an axial-flow pump that includes guide vanes, impelle and dischage diffuse. Thee impelles with diffeent hub atio wee eseached. The aticle pesents the pefomance cuves and velocity distibutions behind each of the impelle obtained by computational and expeimental ways at six diffeent capacities. The velocity distibutions behind the detached guide vanes of diffeent hub atio ae also pesented. The computational esults wee obtained using the softwae tools CFX-BladeGenPlus and CFX- TASCflow. The expeimental pefomance cuves wee obtained using the standad pocedue. The expeimental velocity distibutions wee obtained by pobing of the flow. Good coespondence of esults, both fo pefomance cuves and velocity distibutions, was obtained fo most of the consideed cases. As it was demonstated, the pefomance cuves of the pump depend essentially on the impelle hub atio. Velocity distibutions behind the impelle depend stongly on the impelle hub atio and capacity. Conclusions concening these dependencies ae dawn. Keywods: axial-flow pump, guide vanes, impelle, pefomance cuves, velocity distibutions, CFX-TASCflow. 1. Intoduction Axial-flow submesible pumps ae widely used in Ukaine, in paticula, as units of pump stations fo land iggiation and dainage. Nowadays, these stations ae completed with impoted pumps, as Ukainian entepises do not poduce such pumps. In USSR, such pumps wee developed 30 yeas ago and wee poduced by the factoies Ualhydomash (Russia) and Moldavhydomash (Moldova). Quality of thei design does not coespond to the moden scientific and technical level. Taking into account lage industial, scientific and technical potential of Ukaine, it would be expedient to oganize hee own poduction of such pumps. With this pupose, the eseach was conducted at the depatment of applied fluid mechanics, esulted in ceation of a pefected design scheme of such pumps named GV IMP (guide vanes impelle) [1]. As it was shown [2], the ceated pumps have lowe poduction costs, equie lowe maintenance expenses and, at the same time, ensue lage efficiency. And as the pumps of this type ae often of lage powe, efficiency is one of the most impotant citeia of thei pefection. A new scientific idea implemented in design of these pumps is ceation of pe-swil at the entance to impelle, opposite to shaft otation, using guide vanes (these vanes ae

2 2 simultaneously the suppots of the engine capsule). As it was found out [3], pesence of pe-swil upsteam of the impelle influences significantly the pefomance cuves of the pump, by changing its shape and width of woking capacity ange. This aticle pesents the esults of futhe expeimental eseaches aimed at study of influence of geometical paametes of hydaulic components of the pump upon the flow patten inside it and its pefomance cuves. This will pemit, in paticula, to find out minimum hub atio behind the guide vanes that doesn t cause evese flow nea the hub and find out impelle hub atio that coesponds to the highest pump efficiency. Fo pefoming the computational eseach, we have chosen the softwae package CFX-TASCflow (http://www-wateloo.ansys.com/cfx/), as accoding to the eview [4], this package is one of the most espected CFD tools fo simulation of fluid flows in hydaulic machiney. As fo the expeimental eseach, pefomance cuves of the pump wee obtained using the standad pocedue. Besides, we have pobed the flow downsteam of the impelle with a 5-channel pobe at diffeent capacities, thus having obtained expeimental distibutions of velocities at diffeent modes of pump opeation. 2. Desciption of the expeimental eseach Object of eseach. Fo pefoming the eseach, a model pump was designed, which hydaulic components ae pesented at Fig. 1. Those hydaulic components wee guide vanes, impelle and dischage conical diffuse. Guide vanes (Fig. 2) include five cylindical vanes of 4 mm in thickness, with plane initial section of 15 mm in length. Radius of cylindical suface used fo shaping a vane was 60 mm, spanning angle was 84, i.e., the inlet edge of each vane was installed steamwise, wheeas the outlet edge was almost pependicula to the flow. Diamete of each impelle was 180 mm. Each of tested impelles had 4 blades designed accoding to the method of Voznesensky Pekin [5] fo conditions of axial outflow and constant velocity moment of flow upsteam of impelle. Impelles diffeed by the hub atio đ hub, 9 and 8 coespondingly. Fist two impelles wee designed basing upon the meidional pojection fo the fist impelle and, thus, had equal blade pofiles. The thid impelle was designed basing upon its own meidional pojection. Dischage diffuse was conical in shape and had aea atio of 1.72 and intenal angle of 24. Accoding to the esults of the pape [6], the losses in the dischage diffuse of this pump ae minimal just with this intenal angle. Figue 1. Meidional view of the investigated model pump of GV IMP type

3 3 Figue 2. Guide vanes, impelle and dischage diffuse (photo) Methods of eseach. Pefomance cuves of the pump wee obtained by standad test pocedue. The flow patten downsteam of impelle was pobed using a 5-channel pobe. The section of pobing was located just behind the impelle blades (Fig. 1). Diffeence in capacity measued with a diaphagm and computed using the esults of pobing did not exceed 6%. Desciption of the pobing pocedue and fomulas fo computation of capacity ae pesented in [7]. 3. Desciption of the computational eseach Fo pefoming the computational eseach, we have used the softwae package CFX- TASCflow. The geneal sequence of actions and sepaate softwae tools ae descibed below. CFX-BladeGen. Fo ceation of solid models of hydaulic components, we have used the softwae tool CFX-BladeGen. The models of guide vanes and impelle (togethe with the dischage diffuse) wee ceated sepaately. The inteface of CFX-BladeGen has allowed fo input conveniently of all the data fom the theoetical dawing of an impelle. Impelle blades wee specified by a set of dawing views of pofiles. Each pofile was obtained at sections of a blade by cylindical sufaces of diffeent adius. The window of CFX-BladeGen is pesented at Fig. 3. CFX-BladeGenPlus. Afte ceation of solid models of guide vanes and impelles, we have computed flow field inside these components using the softwae tool CFX- BladeGenPlus. This softwae tool is featued with easy undestandable inteface convenient fo an enginee without special knowledge in the CFD. Befoe computation of flow in CFX-BladeGenPlus, unstuctued mesh with tetahedon cells is geneated. We used the meshes containing about cells. As souce data, fluid popeties, capacity, otational speed and inlet velocity pofiles wee specified. When computing the flow though guide vanes, we assumed that the upsteam flow does not swil and is of constant velocity though the inlet section. When computing the flow though impelles, we specified at the inlet the velocity distibutions obtained by pobing the flow behind guide vanes (to be moe exact, behind the impelle with the blades emoved these distibutions ae pesented at Fig. 5). As a esult of computation, we obtained the distibution of velocities and pessue though the whole space inside the hydaulic component. We obtained also the integal paametes of flow: axial foce and toque imposed on blades, loss facto (fo guide vanes), as well as head, consumed powe and efficiency (fo impelles). The fomulas fo computing these paametes ae editable by a use. Note, howeve, that the softwae tool CFX-BladeGenPlus, being a vey convenient tool fo expess analysis of flow, has esticted possibilities. This tool is designed fo computation of flow in detached hydaulic components, not allowing fo simulation of flow in the whole flow passage. In this tool, only an algebaic eddy-viscosity tubulence

4 4 model is implemented, which is too simplified appoach fo complex flows. Besides, this tool does not allow fo simulation of flows with seveal phases, heat tansfe and othe effects that equie additional model equations. Fo such poblems, CFX-TASCflow should be used. Figue 3. Window of the softwae tool CFX-BladeGen. In the window, the geometical model of the impelle with hub atio of 9 is pesented. The dependencies below (blade angles and blade thickness vs. distance along the blade chod) elate to the pofile located at the hub. CFX-TuboGid. Befoe computation of flow in CFX-TASCflow, computational mesh should be geneated. A convenient tool fo geneating the mesh in the bladed components is the softwae tool CFX-TuboGid. As souce data, this tool takes the files ceated in CFX-BladeGen, and saves the geneated mesh in the fomat equied fo CFX- TASCflow. CFX-TuboGid geneates stuctued meshes with hexahedon cells. The computational domain that coesponds to a sepaate hydaulic component (guide vanes o impelle) is split into blocks (sub-domains), accoding to the topology of splitting selected by use. Afte selection of the topology, the use coects manually the position of sub-domains, laws of node distibution along gid lines, position of contol points, accoding to the ecommendations descibed in the use manual of CFX- TuboGid [8]. Each of the topologies implemented in CFX-TuboGid [8] suits mostly fo a cetain class of bladed components, poviding the possibility to geneate highquality computational mesh with minimal skew of cells. In this eseach, we used the following gid topologies: fo guide vanes High Stagge Blade Template, fo impelles Single Block Gid Template. The obtained meshes ae pesented at the Fig. 4. Diagnostics of the geneated mesh fo the guide vanes: total numbe of cells is , minimal angle is 20.0, maximal angle is The mesh fo the impelle with đ hub = 9: total numbe of cells is , minimal angle is 24.2, maximal angle is

5 Thus, the quality of geneated meshes is good enough fo unning the numeical simulation. Figue 4. Computational mesh fo guide vanes (left-hand side) and impelle (ight-hand side) fo cleaness, only the gid at medium flow suface in one of blade-to-blade channels is shown CFX-TASCflow. Fo subsequent actions, the softwae tool CFX-TASCflow was used. Fistly, we need to compose the integal computational domain fom the sepaate subdomains that coespond to guide vanes and impelle (togethe with the dischage diffuse). The coesponding computational meshes geneated by CFX-TuboGid (Fig. 4) ae joined thus foming the united computational mesh. At the inteface between guide vanes and impelle, we used the condition of Stage Aveaging [4, 9]. Thus, at this suface, the paametes of flow wee aveaged in the cicumfeential diection. In this eseach, we used k ε tubulence model with scalable wall functions. The desciption of this model and futhe efeences ae pesented, e.g., in [4] and [9]. As the souce data fo unning the simulation, like as in CFX-BladeGenPlus, capacity, otational speed and fluid popeties wee specified. The flow upsteam of guide vanes was assumed non-swiling, of constant velocity though the inlet section. Fo tubulence model equations, medium level of tubulence was specified at the inlet (though, vaiation of this paamete in the wide ange almost did not tell upon the esults of computation). Zeo wall oughness fo the whole flow passage was specified. Fo simplicity, the gap between impelle blades and stato walls was assumed to be zeo. 4. Results of pobing of flow behind the guide vanes Figue 5 pesents compaison of velocity distibutions in the section behind guide vanes obtained numeically with CFX-BladeGenPlus and expeimentally by pobing (the section of pobing was the same, only impelle blades wee emoved). The expeimental esults of Fig. 5 wee ealie published in the pape [10]. Distibutions of axial V z and cicumfeential V u velocity ae given as atio to the aveage (though the section) axial velocity. As one can see, no sepaation of flow is obseved fo all the hub atios investigated. Distibution of cicumfeential velocity coesponds appoximately to the law of constant velocity moment, V u = const. The numeical and expeimental velocity pofiles coincide qualitatively, though with some quantitative discepancy. The swil intensity obtained by

6 6 computation exceeds the expeimental value. In ode to check gid independence of the solution, this flow was computed using meshes of , and cells. The maximum diffeence in local values of velocities did not exceed 5% fom the axial velocity aveage though the section. V z V z V z Figue 5. Distibutions of axial (left-hand side) and cicumfeential (ight-hand side) velocities: expeiment: hub atio of, 9, 8 (thin lines ae fo visual aid only); computation with CFX-BladeGenPlus pale solid line 5. Pefomance cuves of the pump and flow patten behind the impelle at diffeent capacities Dependence of theoetic head of the impelle on capacity. As the tool CFX- BladeGenPlus allows fo flow simulation only in detached components, we povide compaison with the expeimental esults by the theoetic head poduced by an impelle. Theoetic head is the head divided by hydaulic efficiency. This dependence of theoetic head on capacity obtained fom the numeical and V u V u V u

7 7 expeimental esults is pesented in the non-dimensional fom at Fig. 6. The aveage divegence of theoetic head obtained with CFX-BladeGenPlus and expeimentally fo the investigated ange of capacity was 10%, the maximal divegence was about 20%. Theoetic head obtained with CFX-TASCflow coincided with the expeimental values still bette. kh 0 kh kq kq kh kq Q K Q = 3 nd H K H = n 2 D 2, Q capacity, H head, n otational speed, ps, D impelle diamete Figue 6. Dependence of theoetic head on capacity fo the investigated impelles: expeiment: impelle hub atio of, 9, 8; computation with CFX-BladeGenPlus pale solid line; computation with CFX-TASCflow dashed line, Pefomance cuves of the pump. These cuves obtained numeically and expeimentally fo the whole flow passage of the pump ae pesented at Fig. 7. Computation of flow using CFX-TASCflow was pefomed fo the same capacities at which pobing of flow was pefomed. As one can see, fo the whole investigated ange of capacities, the pefomance cuves coespond with each othe qualitatively quite well, and in most cases, good quantitative coespondence is also obseved. Fig. 7 pesents also the dependence of impelle efficiency on capacity obtained with CFX-BladeGenPlus. The obtained values of efficiency ae believable and agee well with the impelle efficiencies obtained using CFX-TASCflow (not shown). As fo the pefomance cuves, the following may be obseved. As the capacity of pump inceases, the head deceases, and the powe inceases, as is typical fo adial-flow pumps. The lage is the impelle hub atio, the moe extended ae pefomance cuves of the pump along capacity axis. The lagest efficiency was obtained fo the impelle hub atio of 9, howeve, in this case, capacity ange with high level of efficiency was the naowest. The lagest consumed powe was also obtained fo the impelle hub atio of 9.

8 8 k H, k N k H K N Eff Eff 0 0 Impelle with the hub atio of, the modes fo which pobing was pefomed: 1 K Q = 9; 2 K Q = 1; 3 K Q = 1; 4 K Q = 2; 5 K Q = 6; 6 K Q = k Q 1.20 k H, k N k H K N Eff Eff 0 0 Impelle with the hub atio of 9, the modes fo which pobing was pefomed: 1 K Q = 3; 2 K Q = 6; 3 K Q = 0; 4 K Q = 2; 5 K Q = 6; 6 K Q = k Q 1.20 k H, k N k H K N Eff Eff 0 0 Impelle with the hub atio of 8, the modes fo which pobing was pefomed: 1 K Q = 6; 2 K Q = 2; 3 K Q = 4; 4 K Q = 3; 5 K Q = 4; 6 K Q = k Q 1.20 Figue 7. Dependence of head, powe and efficiency on capacity of the pump: solid lines expeiment pefomance cuves obtained using the standad technique; painted makes expeiment the modes fo which pobing was pefomed: impelle hub atio of, 9, 8; blank makes computation, CFX-TASCflow; pale line impelle efficiency, computation, CFX-BladeGenPlus

9 9 Maximum efficiency achieved with each of these impelles, accoding to the expeimental esults, is 70%, 73% and 67%, and accoding to the computational esults, is 68%, 67% and 62% coespondingly. Accoding to the expeiment, maximum efficiency fo the impelle with đ hub = is eached at the mode 3, fo the impelle with đ hub = 9 at the mode 4 and fo the impelle with đ hub = 8 at the mode 5. Accoding to the computation, maximum efficiency fo each impelle is eached at the mode 5. Bladed components of this pump ae designed in such a way that behind the impelle it would be no swil at the nominal capacity. While passing between guide vanes, the flow obtains lage negative swil, of appoximately constant velocity moment though the section. As the flow passes though impelle, its velocity moment changes to zeo. As a esult of this, the head is ceated. At the capacities above nominal, the flow afte passing though the impelle keeps its negative swil and, thus, it swils downsteam in the diection opposite to shaft otation. At the capacities below nominal, the flow afte passing though the impelle gets positive swil and, thus, it swils downsteam in the same diection as the shaft. Coesponding flow pattens in absolute fame of efeence obtained with CFX-TASCflow ae shown at Fig. 8. The moe the capacity diffes fom the nominal, the lage is swil in the dischage diffuse. Figue 8. Velocity vectos of the flow inside the pump at the modes 1 (left-hand side) and 5 (ight-hand side) Velocity distibutions behind the impelle. These distibutions obtained by computation using CFX-TASCflow and by pobing of flow ae pesented at Fig. 9. Distibutions of axial V z and cicumfeential V u velocity fo each impelle ae given as atio to the aveage (though the section) axial velocity at the nominal capacity fo the same impelle. Non-dimensional cicumfeential velocity at the hub otating togethe with impelle, fo the mentioned impelles, is 1.31, 1.21 and 1.12 coespondingly. Expeimental esults of Fig. 9 at the modes 2, 3 and 4 wee ealie published in [10]. As may be seen, the esults obtained with CFX-TASCflow, in geneal, coincide with the expeimental esults quite well, with pope eflection of changes in velocity distibutions at diffeent capacities. The quantitative coespondence of esults is also athe good. Significant discepancies ae obseved mostly fo the impelle with đ hub = 8 and fo vey low capacities, as stong swil pesent in the flow passage in these cases is difficult to be simulated popely and equies advanced tubulence modeling. The following effects ae peculia to these distibutions. Mode 1. Lage esidual swil ceated by guide vanes is available. The flow is pessed to the peiphey, especially distinctly behind the impelle with đ hub = 8, whee lage stagnation egion is obseved nea the hub.

10 10 Mode 1 (the lagest capacity, the head is close to zeo): Vz Vz Vz Mode 2 (the ight bound of the woking ange): Vz

11 11 Vz Vz Mode 3 (the middle of the woking ange): Vz Vz

12 12 Vz Mode 4 (the left bound of the woking ange): Vz Vz Vz

13 13 Mode 5 (low capacity, the mode to the ight-hand side fom the pit ): Vz Vz Vz Mode 6 (the lowest capacity, the mode to the left-hand side fom the pit ): Vz

14 Vz Vz Figue 9. Distibutions of axial (left-hand side) and cicumfeential (ight-hand side) velocity component behind the impelle: expeiment impelle hub atio of, 9, 8 (thin lines ae fo visual aid only); dashed line computation, CFX-TASCflow Mode 2. At this mode, the flow swiled by guide vanes is also not completely deswiled afte passing the impelle. Fo each of impelles, the cicumfeential velocity V u < 0. Axial velocity distibution behind each of thee impelles is distinctly pessed to the peiphey. Behind the impelle with đ hub =, it is the most unifom though the section, and behind the impelle with đ hub = 8, it is the most defomed. Mode 3. At this mode, the swil of flow behind the impelle is the closest to zeo. Peak of the axial velocity obseved at the pevious mode hee is less distinct. On the othe side, peak of the axial velocity nea the hub is obseved. It is most distinct behind the impelle with đ hub = and meely obsevable (accoding to the expeimental esults) behind the impelle with đ hub = 8. Mode 4. At this mode, the flow swiled by guide vanes is e-swiled afte passing the impelle in the diection of shaft otation. Fo each of thee impelles, the cicumfeential velocity V u > 0. Peak of axial velocity at the peiphey is completely smoothed away at this mode behind the impelle with đ hub = (accoding to the expeimental esults) but is still distinctly expessed behind the impelle with đ hub = 8. The flow behind the impelle with đ hub = is stongly pessed to the hub. The stagnation zone behind the impelle with đ hub = 8 that was obseved nea the hub at the pevious modes, now is absent (though this fact is not confimed by computation). Behind the impelle with đ hub = 9, peaks of axial velocity at the peiphey and nea the hub ae appoximately equal (accoding to the computation, tendency fo alignment of peaks is obseved). Mode 5. Lage swil of flow in the diection of shaft otation is available. Cicumfeential velocity is almost constant though the section. In the axial velocity distibution, a shaply expessed peak nea the hub is available (except fo the impelle with đ hub = 8).

15 15 Mode 6. In compaison with the pevious mode, the intensity of flow swil has stengthened. Distibutions of both axial and cicumfeential velocities have essentially changed and pessed to the peiphey. Flow patten has become simila to the solid body type of otation. Note, at the head cuve of the pumps (Fig. 6), between the modes 5 and 6, a pit is available (capacity ange featuing with educed head and unstable flow inside the pump). Pesence of the pit can seemingly be explained by estuctuing of flow inside the pump. At the capacities to the ight fom the pit, the axial velocity distibution is pessed to the hub, so as at the capacities to the left fom the pit it is pessed to the peiphey. Futhe downsteam, the axial velocity distibution is gadually smoothed appoaching finally logaithmic shape typical fo developed tubulent flow in a pipe. Pocess of smoothing of the velocity distibution may be imagined as supeposition of flow of constant (though the section) velocity and votex flow which deceleates apidly moving fluid layes and acceleates slowly moving fluid layes (Fig. 10). In this epesentation, when the mode of pump opeation changes fom 5 to 6, this votex (that smoothes the axial velocity distibution downsteam of impelle) changes the diection of otation (consideing the meidional pojection of the pump). Hee is the explanation of instability of pump opeation at the capacities within the pit : this votex otates sometimes in one diection, sometimes in the opposite diection. Figue 10. Scheme of flow behind the impelle at the mode 6 (left-hand side to the left fom the pit ) and 5 (ight-hand side to the ight fom the pit ); the dak figues epesent distibutions of the axial velocity In the impelle with đ hub = 8, the fluid flow is pessed to the peiphey in the whole capacity ange (Fig. 9). Coespondingly, at the head cuve of the pump with this impelle, thee is no pit (Fig. 7). 6. Conclusions As a esult of this eseach, good coespondence of computational esults obtained using the softwae package CFX with expeimental esults was obseved, except fo stongly swiled flows. Namely, with CFX-BladeGenPlus the pefomance cuves of the pump and velocity distibution behind the guide vanes wee ageed, with CFX-TASCflow the pefomance cuves and velocity distibution behind the impelles. The following conclusions can be also dawn: - When hub atio behind the guide vanes of this design is 8, the evese flow behind the guide vanes is still absent. - Flow swil behind the impelle depends stongly on the capacity of pump. At capacities above nominal, the esidual swil geneated by guide vanes is available behind the impelle. At low capacities, the impelle foces the flow to swil in the diection of shaft otation. - Distibution of the axial velocity behind the impelle also depends significantly on the capacity. At high capacities, fluid flow is pessed to the peiphey. As the capacity deceases till the mode to the ight fom the pit on the head cuve, the flow is

16 16 gadually depessed fom the peiphey and pessed to the hub. At vey low capacities (to the left fom the pit ), the flow is stongly pessed to the peiphey. - Distibution of the axial velocity behind the impelle also depends on the impelle hub atio. At the hub atio of 8, the flow is pessed to the peiphey in the whole ange of capacities. - Shape of pefomance cuves obtained in this axial-flow pump with lage negative inlet swil is typical fo adial-flow pumps (as the capacity inceases, the head deceases and the powe inceases). - As the impelle hub atio inceases, its pefomance cuves extend along the capacity axis. - The highest efficiency (expeiment 73%, computation 68%) was eached at the impelle hub atio of 9 (expeiment; computation ). Howeve, in this case, the ange of capacities of high efficiency was the naowest. - The lagest consumed powe was also obseved at the impelle hub atio of 9 (expeiment; computation ). - In the pumps with impelle hub atios of and 9, a distinctly expessed pit was obseved at pefomance cuves. At the impelle hub atio of 8, this pit was absent. - Accoding to the expeiment, in the pump with the impelle hub atio of, the highest efficiency was eached at appoximately zeo swil behind the impelle. At the hub atio of 8, the highest efficiency was obtained at lage positive swil behind the impelle, i.e., at a significantly lowe capacity. Accoding to the esults of computation with CFX-TASCflow, fo each of impelles the highest efficiency was eached at athe lage positive swil behind the impelle. Acknowledgements The pesent eseach was conducted unde suppot of the collective of the depatment of fluid mechanics of Sumy State Univesity. Refeences [1] Gusak A. G. and Yevtushenko A. A On Expediency and Pinciples of Ceation of a Dimension-Type Seies of Submesible Monoblock Pumps Designed as Guide Vanes Impelle Hydaulic and Pneumatic Machines and Units. Theoy, Calculation, Design: Collection of Papes / Ed. by I. A. Kovalyov Kiev: ISIO. P (in Russian) [2] Gusak A. G Pefecting of Hydaulic Components of Submesible Monoblock High-Speed Pump Units Abstact of Ph.D. thesis Sumy: Sumy State Univesity 21 p. (in Russian) [3] Bulaka V. B., Gusak A. G. and Yevtushenko A. A Influence of Swil Velocity Moment of Flow Upsteam of Impelle upon Head and Pefomance Cuves of an Axial-Flow Pump Vestnik NTUU KPI, Kiev. No. 36, Vol. 1. P (in Russian) [4] Kochevsky A. N. and Nenya V. G Contempoay Appoach fo Simulation and Computation of Fluid Flows in Centifugal Hydomachines Vestnik SumSU, Sumy. No. 13 (59) P (in Russian) [5] Lomakin A. A Radial-Flow and Axial-Flow Pumps Mashinostoyenie, Moscow, Leningad. 364 p. (in Russian) [6] Kochevsky A. N Investigation of Swiling Flow in Diffuses Installed at the Exit of an Axial-Flow Pump TASK Quately No. 4. P [7] Kochevsky A. N. and Kochevsky N. N Expeimental Investigation of Flow Patten behind an Impelle of Axial-Flow Pumps Vestnik SumSU, Sumy. No. 9 (30) 10 (31) P (in Russian) [8] CFX-TuboGid Softwae Documentation. Use Manual. Vesion p. [9] CFX-TASCflow Computational Fluid Dynamics Softwae. Theoy Documentation. Vesion p. [10] Yevtushenko A. A., Fedotova N. A. and Kochevsky A. N Expeimental Investigation of Flow Patten in the Meidional Pojection of an Impelle of a Pump of GV IMP Type Vestnik NTUU KPI, Kiev. No. 42, Vol. 2. P (in Russian)

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