Research on the Simplified Design of a Centrifugal Compressor Impeller

applied sciences

Article Research on the Simpliﬁed Design of a Centrifugal Compressor Impeller Based on Meridional Plane Modiﬁcation

Hong Xie ID , Moru Song, XiaoLan Liu, Bo Yang * and Chuangang Gu

School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China; [email protected] (H.X.); [email protected] (M.S.); [email protected] (X.L.); [email protected] (C.G.) * Correspondence: [email protected]; Tel.: +86-21-3420-6871

Received: 7 July 2018; Accepted: 6 August 2018; Published: 10 August 2018

Abstract: This study mainly focuses on investigating the influence of meridional contour of a steam centrifugal compressor on aerodynamic performance. An optimal design method is put forwards, in which the hub-line on the meridional plane is modified and optimized. Based on the data from numerical simulation, aerodynamic characteristics are compared in detail among a prototype and three modified impellers. It is shown that stall margin of the optimized impeller can be enlarged by approximately 50%, though at design point efficiency and pressure ratio is decreased a little bit. Under the working conditions with low flow rate, the optimized impeller exhibits the best performance compared with the prototype and two other impellers. Furthermore, numerical result is validated by the experiment and is matched the measure data very well.

Keywords: steam centrifugal compressor; optimal design; hub-line

1. Introduction Aerodynamic and structural design of an impeller are important to the performance of a compressor unit [1]. The design work of a new impeller is mainly focused on the designing of flow passage [2]. Meridional plane design is one of the important parts of the flow passage design. The geometrical profiles of impeller hub and shroud have significant effects on the overall performance of a compressor. This is because the fluid flowing between these two curves not only determines the efficiency of the impeller but also strongly affects the performance of diffuser or volute in downstream [3]. Much progress had been made in last decades [4]. One of the most outstanding works was from Jansen [5], who applied the inverse design methods to the flow passage design in turbomachinery. With recent improvement, the advanced optimization methods have been introduced into the design of meridional profiles. Casey [6] and Wang [7] put forward a method to define the meridional channel by a string of Bezier points. This method based on Bernstein-Bezier polynomial patches had already been a guideline of the parameterization of the meridional plane profile. Borges [8] described a kind of three-dimensional inverse method, by which an imposition of mean swirl was defined as optimization specification throughout the meridional section of the turbomachinery. Benini [9] explored an evolutionary optimization algorithm to optimize meridional geometry, by which the secondary flows across the impeller could been reduced greatly. A numerical method coupled with the optimization design methodology, which was consisted of reaction surface method (RSM), statistical approach and genetic algorithm, was developed to obtain optimized hub and shroud line by Sun [10]. Meanwhile, Cho [11] used an evolutionary algorithm with the help of a Bezier curve to make efficiency higher without the reducing of the pressure ratio. As some extra mechanical constraints, such as the maximum stress and stress distribution, had to be considered in the aerodynamic

Appl. Sci. 2018, 8, 1339; doi:10.3390/app8081339 www.mdpi.com/journal/applsci Appl. Sci. 2018, 8, 1339 2 of 16 design, the multidisciplinary and global optimization design methods were presented in resent literature. A software using a through-flow computation with a breeder genetic algorithm had been programmed to acquire the optimization of meridional plane [12]. Mueller [13] presented a multidisciplinary and multi-objective optimization system based on an artificial neural network to improve the performance of the impeller while the mechanical stresses were kept within the limitation. A traditional meridional profile was usually described by several arc lines, and widely adopted in the most of meridional shape design. It was generally believed that for the shroud line and the hub-line on the meridional plane, the arcs and the smoothed connection among these arcs were beneficial to aerodynamic performance. However, during the process of the manufacturing of a compressor unit, it would take most of time to produce this kind of 3D complex impeller with high cost by a 5-axis machine. In order to save time and cost, welding technology is gradually being used in manufacturing of impellers. It is due to the narrowed shrouded structure that the work of welding blades on the disk is very hard. So, a simplified meridional profile of an impeller is needed urgently to substitute the traditional meridional profile. But, although much improvements on impeller design, such as blade profiles, incidence angle and stagger angle, etc., had been greatly achieved, there was not enough attention on how to simplify the impeller structure to adapt to the welding manufacture. Therefore, in this paper, a simplified geometrical configuration of the meridional contours is presented, which can simplify the structure of the impeller and be beneficial to the welding manufacture with a little negative effect on the impeller performance.

2. Meridional Shape Design In this study, an industrial impeller of a steam compressor is used as a prototype. Its design parameters are listed in Table1.

Table 1. Design parameters of prototype impeller.

Parameters Unit Value Inlet total pressure kPa 94.3 Inlet total temperature K 371.15 Mass ﬂow rate kg/s 2.37 Total-to-total pressure ratio - 1.4 Number of impeller blades - 12/12 main/splitter blades Impeller inlet tip diameter, D1 m 0.3464 Impeller outlet diameter, D2 m 0.897 Design rotational speed rpm 5600 Exit blade angle (meridional) deg 0

The meridional cross-section of the prototype impeller is shown in Figure1. The impeller was initially designed with the shrouded structure due to the large outlet diameter, and arc line was used to deﬁne the hub and shroud line. Thus, there would have some potential problems during manufacture for the reasons as alluded in the above words. The hub-line is divided into three segments, such as inlet line, middle line and exit line, as shown in Figure1. The inlet line and middle line are arc line which can be parameterized by Bezier curve method, and exit line is a straight line. These three lines are smoothly connected by two points one by one as shown in the ﬁgure. The slope distribution of the hub-line is shown in Figure2. Figure2 shows the relationship between slope of the hub-line and axial height of hub-line. These two interrupt points, at which the slope of the hub-line is varied severely, are selected as the break points. Appl. Sci. 2018, 8, 1339 3 of 16 Appl. Sci. 2018, 8, x FOR PEER REVIEW 3 of 16 Appl. Sci. 2018, 8, x FOR PEER REVIEW 3 of 16 Appl. Sci. 2018, 8, x FOR PEER REVIEW 3 of 16

FigureFigure 1.1. MeridionalMeridional cross-section.cross-section. Figure 1. Meridional cross-section. Slope Slope 100 Slope 100 100 90 90 90 80 80 80 70 70 70 60 60 60 50

Deg 50

Deg 40 40 40 30 30 30 20 20 20 10 10 10 0 20406080100 0 20406080100 0 20406080100Normalized hub length(% m) Normalized hub length(% m) Normalized hub length(% m) FigureFigure 2.2. SlopeSlope distribution.distribution. FigureFigure 2.2. SlopeSlope distribution.distribution. InIn orderorder toto observeobserve thethe effecteffect ofof hub-linehub-line profileprofile onon thethe machinemachine performance,performance, threethree modifiedmodified InIn orderorder toto observeobserve thethe effecteffect ofof hub-linehub-line proﬁleprofile onon thethe machinemachine performance,performance, threethree modiﬁedmodified impellersimpellers areare introducedintroduced inin thisthis paper.paper. AsAs shownshown inin FigureFigure 3,3, thethe threethree modelsmodels areare thethe inletinlet lineline impellersimpellers areare introduced introduced in in this this paper. paper. As shownAs shown in Figure in Figure3, the three3, the models three models are the inletare linethe changedinlet line changedchanged modelmodel (LA),(LA), middlemiddle lineline changedchanged modelmodel (AL)(AL) andand bothboth inletinlet lineline andand middlemiddle lineline changedchanged modelchanged (LA), model middle (LA), line middle changed line model changed (AL) model and both (AL) inlet and line both and inlet middle line and line middle changed line model changed (LL). modelmodel (LL).(LL). And,And, otherother geometricalgeometrical parametersparameters inin thesethese threethree impellersimpellers suchsuch asas bladeblade angle,angle, backback And,model other (LL). geometrical And, other parameters geometrical in theseparameters three impellers in these suchthree as impellers blade angle, such back as blade sweep angle, angle, back etc., sweepsweep angle,angle, etc.,etc., areare keptkept thethe samesame asas thosethose ofof thethe prototype.prototype. ItIt isis obviousobvious ththatat linearlinear lineslines areare muchmuch aresweep kept angle, the same etc., asare those kept ofthe the same prototype. as those Itof is the obvious prototype. that linearIt is obvious lines are that much linear simpler lines are than much the simplersimpler thanthan thethe BezierBezier curve.curve. Beziersimpler curve. than the Bezier curve.

((aa)) LALA ((bb)) ALAL ( (cc)) LLLL (a) LA (b) AL (c) LL FigureFigure 3.3. ComparationComparation ofof meridionalmeridional sectionssections amongamong threethree modifiedmodified impellers.impellers. ((aa)) LALA == inletinlet lineline Figure 3. Comparation of meridional sections among three modified impellers. (a) LA = inlet line changedFigurechanged 3. model;model;Comparation ((bb)) ALAL of== middlemiddle meridional lineline changed sectionschanged among model;model; three andand ((c modiﬁedc)) LLLL == bothboth impellers. inletinlet lineline (a )andand LA middlemiddle = inlet line line changed model; (b) AL = middle line changed model; and (c) LL = both inlet line and middle line changedchanged model. model;model. (b) AL = middle line changed model; and (c) LL = both inlet line and middle line changedchanged model.model.

Appl. Sci. 2018, 8, 1339 4 of 16

3. Numerical Methods In this study, a commercial software, Numeca FineTM/Turbo [14], is applied to the impeller performance analysis based on a 3-D steady and unsteady compressible finite volume scheme. It is assumed in the simulation that internal flow in impeller is relatively stable three-dimensional viscous compressible turbulent flow. The governing equations are continuous equation including Reynolds-averaged Navier-stokes equation, energy conservation equation, the ideal gas state equation [15]. The governing equations written in a Cartesian frame can be expressed as follows:

 →  ∂ρ  + ∇• ρV = 0  ∂t  ∂ → →→ → ↔ ρV + ∇· ρVV = ρ F − ∇·p + ∇· τ , (1) ∂t   ∂E → → → ↔ →  + ∇· (E + P)V = ρ F ·V + ∇· τ ·V + ∇·(k∇T)  ∂t

→ → ↔ where, ρ is flow density, t is time, V is velocity vector, F is external force, p is external pressure, τ is viscous stress, E is internal energy, P is kinetic energy, k is adiabatic index and T is temperature. The ideal gas state equation is: p = ρRT, (2) where, R is gas constant. Supplementary equations are expressed as:  e = C T  v h = e + pV , (3)  TdS = de + pdV where, e is total energy, Cv is the specific heat at constant volume, h is enthalpy of fluid and S is entropy. The employed turbulence modelling to consider the compressibility is the Spalart–Allmaras model [16]. The Spalart–Allmaras (S–A) turbulence model contains a set of relatively new single equation, which ∼ uses an eddy-viscosity variable v, and is combined with speed, precision and stability, the turbulent eddy transport equation. This can be expressed as follows [17]:

 ( ∼ ) ∼ !2 ∂ ∼ ∂ ∼ 1 ∂ ∼ ∂v ∂v ρv + ρvui = Gv +  µ + ρv + Cb2ρ  − Yv, (4) ∂t ∂x σ∼ ∂x ∂x ∂x i v j j j where, G is production of turbulent viscosity, σ∼ and C are model constants, v is molecular kinematic v v b2 ∼ viscosity, v is turbulent viscosity, µ is dynamic viscosity, x is cartesian coordinate and Yv is reduction of turbulent viscosity, which happens near the wall. In the upstream and downstream, the computational domain of single flow passage is extended as shown in Figure4a. The number of grid points for a single passage is around 1,250,000, which is large enough according to the grid independence investigation. y+ is small enough for the S–A turbulence model. The enlarged detail mesh figure around blade leading edge is shown in Figure4c. A single passage model with periodical boundary conditions is used in steady simulation. Velocity direction, absolute total pressure and total temperature are imposed at the inlet boundary, outlet mass-flow and initial pressure on the outlet boundary. In this study, the working point close to stall condition is figured out by the lowest mass flow, with which the numerical simulation can reach convergent results. Appl.Appl. Sci. Sci. 20182018,, 88,, x 1339 FOR PEER REVIEW 55 of of 16 16 Appl. Sci. 2018, 8, x FOR PEER REVIEW 5 of 16

(a) Blade to blade mesh (b) 3D mesh (c) Leading edge mesh (a) Blade to blade mesh (b) 3D mesh (c) Leading edge mesh Figure 4. Mesh of single flow passage. Figure 4. Mesh of single flow passage. Figure 4. Mesh of single flow passage. The LL(both inlet line and middle line changed model) impeller is chosen to analyze the steady and unsteadyTheThe LL(both LL(both performance inlet inlet line line and andwith middle middle the help line line of changed changedthe full passage model) model) impellermodel. impeller The is is chosen chosenreason to towhy analyze analyze the LL the the impeller steady steady andisand chosen unsteady unsteady to be performance the optimized with impeller thethe helphelp will ofof be thethe introduced fullfull passagepassage in the model. model. following The The reason reason sections. why why In the thethe LL LLfull impeller impeller passage is ismodel,chosen chosen tothe to be bevolute the the optimized optimized with an impellerasymmetrical impeller will will be beconfiguration introduced introduced in inis thethe considered followingfollowing as sections.sections. shown In in the Figure full full passage passage5. The model,numbermodel, the of the volutevolute grid with withpoints an an asymmetricalof asymmetricalthe whole flow configuration configuration passage model is considered is isconsidered about as 45 shown million,as shown in Figurewhich in 5 Figureis. Thedetermined number 5. The numberbyof thethe gridgrid of the pointsindependent grid of points the whole research.of the flowwhole And, passage flow frozen passage model roto ismodelr abouttechnique is 45about million, is used45 million, which to deal which is determinedwith is the determined interface by the bybetweengrid the independent grid impeller independent and research. volute. research. And, frozen And, rotorfrozen technique rotor technique is used is to used deal withto deal the with interface the interface between betweenimpeller impeller and volute. and volute.

(a) Full passage model (b) Tongue model (a) Full passage model (b) Tongue model Figure 5. Mesh of full flow passage. FigureFigure 5. 5. MeshMesh of of full full flow flow passage. passage. Meanwhile, LL impeller is selected to be the experiment object. Figure 6 shows 2D cross-section of geometricMeanwhile, structure LL impeller of experimental is selected impeller,to be the experimentas is shown, object. the hub Figure contour 6 shows is consisted 2D cross-section of three Meanwhile, LL impeller is selected to be the experiment object. Figure6 shows 2D cross-section of ofstraight geometric line. structureThe hub formingof experimental is made impeller, of three stasainless is shown, steel the plates hub weldedcontour together. is consisted There of threeis no geometric structure of experimental impeller, as is shown, the hub contour is consisted of three straight straightrequirement line. toThe processing hub forming whole is madeimpeller of threeor the st ainlesshub with steel five-axis plates weldedmachine together. as the conventional There is no line. The hub forming is made of three stainless steel plates welded together. There is no requirement to requirementimpeller. The to welding processing place whole has beenimpeller marked or the out hub as shownwith five-axis in Figure machine 6. By this as thekind conventional of welding processing whole impeller or the hub with five-axis machine as the conventional impeller. The welding impeller.technology, The not welding only does place processing has been time marked and cost out cut as down,shown but in Figurealso the 6. manufacturing By this kind ofof impellerwelding place has been marked out as shown in Figure6. By this kind of welding technology, not only does technology,becomes very not simple. only does Furthermore, processing weight time and of the cost impeller cut down, can butbe reduced also the significantlymanufacturing by ofthe impeller hollow processing time and cost cut down, but also the manufacturing of impeller becomes very simple. becomesdesign of very the hub,simple. which Furthermore, can be advantageous weight of the to impeller the rotor can dynamics be reduced balance significantly and beneficial by the hollow to the Furthermore, weight of the impeller can be reduced significantly by the hollow design of the hub, designbearing of design. the hub, which can be advantageous to the rotor dynamics balance and beneficial to the bearingwhich can design. be advantageous to the rotor dynamics balance and beneficial to the bearing design. Appl. Sci. 2018, 8, 1339 6 of 16 Appl.Appl. Sci. Sci. 2018 2018, ,8 8, ,x x FOR FOR PEER PEER REVIEW REVIEW 66 of of 16 16

FigureFigure 6. 6. 2D2D cross-section.cross-section.

4.4. ResultsResults andand AnalysisAnalysis

4.1.4.1. SingleSingle PassagePassage ModelModel

4.1.1.4.1.1. OverallOverall PerformancePerformance TheThe overall overall performance performance ofof impellersimpellers isis shownshown inin FigureFigure 7.77.. InIn this this study, study, thethe largestlargest massmass ﬂowflowflow raterate (Q/Qd) (Q/Qd) ofof of allall all thethe the impellersimpellers impellers isis is selectedselected selected asas as 1.2.1.2. 1.2. InIn In fact,fact, fact, itit it isis is duedue due toto to lowlow low rotationalrotational rotational speedspeed speed thatthat thisthis kindkind ofof impeller impeller has has an an excellent excellent performance performance underunder thethe workingworking conditionsconditions withwith thethe largelarge massmass rate.rate. So,So, thethe choke choke performance performance will will not notnot be bebe analyzed analyzedanalyzed in inin the thethe followed followedfollowed words. words.words.

prototype prototype prototype prototype AL 1.440 AL AL 1.440 AL LA LA LA 0.92 LA 0.92 LL 1.435 LL LL 1.435 LL

0.91 1.430 0.91 1.430

1.425 1.425 0.90 0.90 1.420 1.420 0.89 0.89 1.415 1.415 Isentropic efficiency

Isentropic efficiency 0.88 1.410 0.88 1.410 Total to total pressure ratio Total to total pressure ratio 1.405 1.405 0.87 0.87 1.400 1.400 0.7 0.8 0.9 1.0 1.1 1.2 0.70.80.91.01.11.2 0.7 0.8 0.9 1.0 1.1 1.2 0.70.80.91.01.11.2 Normalized mass flowrate(Q/Qd) Normalized mass flowrate(Q/Qd) NormalizedNormalized mass mass flowrate flowrate (Q/Qd) (Q/Qd) ((aa)) EfficiencyEfficiency ((bb)) PressurePressure ratioratio

FigureFigure 7. 7. PerformancePerformance curve. curve.

InIn thethe FigureFigure 7a,7a, atat thethe designdesign point,point, thethe LALA impellerimpeller achievesachieves toto thethe highesthighest efficiencyefficiency andand In the Figure7a, at the design point, the LA impeller achieves to the highest efficiency and pressure pressurepressure ratioratio amongamong fourfour impellers,impellers, allall thethe samesame thethe ALAL impellerimpeller hashas thethe lowestlowest efficiencyefficiency andand ratio among four impellers, all the same the AL impeller has the lowest efficiency and pressure ratio. pressurepressure ratio.ratio. MeanwhileMeanwhile itit isis foundfound thatthat forfor thethe LALA andand prototypeprototype impellers,impellers, theirtheir peakpeak efficiencyefficiency Meanwhile it is found that for the LA and prototype impellers, their peak efficiency points are very pointspoints areare veryvery closeclose toto thethe desigdesignn point.point. But,But, whenwhen thethe flowrateflowrate isis decreased,decreased, performanceperformance ofof LLLL close to the design point. But, when the flowrate is decreased, performance of LL impeller appears to impellerimpeller appearsappears toto bebe better.better. be better. InIn thisthis research,research, thethe compressorcompressor characteristicscharacteristics closeclose toto stallstall pointpoint areare evaluatedevaluated byby thethe stallstall In this research, the compressor characteristics close to stall point are evaluated by the stall margin, margin,margin, asas shownshown inin TableTable 2.2. TheThe stallstall marginmargin ((SMSM)) isis defineddefined asas as shown in Table2. The stall margin ( SM) is defined as SM=−=−1/ Q Q , SM1/ Qstallstall, outlet, outlet Q d d , (5)(5)

where, Q is mass flow rate close to the stall point and Q the design flow rate. In Table 2, where, Qstallstall, outlet, outlet is mass flow rate close to the stall point and Qdd the design flow rate. In Table 2, LLLL impellerimpeller hashas thethe largestlargest stallstall margin,margin, whichwhich isis inincreasecrease byby 50%50% comparedcompared withwith thatthat ofof prototype.prototype. Appl. Sci. 2018, 8, 1339 7 of 16

SM = 1 − Qstall,outlet/Qd, (5)

Appl.where, Sci. 2018Qstall, 8,, outletx FORis PEER mass REVIEW flow rate close to the stall point and Qd the design flow rate. In Table7 of 162, LL impeller has the largest stall margin, which is increase by 50% compared with that of prototype. ItIt means means thatthat afterafter the the simplifying simplifying of theof the meridional meridional profile, profile, performance performance at design at design point ofpoint LL impeller of LL impelleris not obviously is not obviously deteriorated deteriorated (efficiency (efficiency and pressure and ratio pressure is decreased ratio byis decreased about 0.5% by compared about 0.5% with comparedthat of the with prototype that of asthe is prototype shown in Figureas is shown7), while in Figure in some 7), respects, while in itssome off-design respects, performance its off-design is performanceimproved somewhat. is improved somewhat.

TableTable 2. 2. StallStall distinction. distinction. Impeller Prototype AL LA LL Impeller Prototype AL LA LL SM 0.17 0.27 0.15 0.29 SM 0.17 0.27 0.15 0.29 SM: stall margin. SM: stall margin. Though LA impeller presents more excellent capability with large mass rate, performance of the LL impellerThough seems LA impeller to be better presents than morethat of excellent another capabilitythree impellers with largewhen mass the machine rate, performance is slipping of into the theLL working impeller conditions seems to be with better low than mass that rate. of another three impellers when the machine is slipping into the working conditions with low mass rate. 4.1.2. Meridional Plane 4.1.2. Meridional Plane The distributions of relative Mach number and pressure coefficient at the design point are shown The distributions of relative Mach number and pressure coefficient at the design point are shown in Figure 8. The pressure coefficient shown is defined as in Figure8. The pressure coefficient shown is defined as = P Cp P , (6) Cp = Ptotal, in , (6) Ptotal,in where, P is the static pressure and Ptotal, in the total pressure at inlet. where, P is the static pressure and Ptotal,in the total pressure at inlet.

Prototype AL impeller LA impeller LL impeller Relative Mach number

(a) Relative Mach number Pressure coefficient

(b) Static pressure coefficient

FigureFigure 8. 8. AerodynamicAerodynamic parameters parameters distribution distribution on on th thee meridional meridional plane plane at at the the design design point. point.

In general, the uniform distribution of Mach number and pressure has a positive impact on In general, the uniform distribution of Mach number and pressure has a positive impact on efficiency and stall margin. But, it is found in Figure 8a that there is a region of high relative Mach efficiency and stall margin. But, it is found in Figure8a that there is a region of high relative Mach number both in AL and LL impeller, which is very close to the turning point of the shroud line. In number both in AL and LL impeller, which is very close to the turning point of the shroud line. In this this region, the pressure is relatively lower, as shown in Figure 8b. So, this kind of nonuniformity of region, the pressure is relatively lower, as shown in Figure8b. So, this kind of nonuniformity of relative relative Mach number and pressure (shown in Figure 8) probably is one of the negative affects which Mach number and pressure (shown in Figure8) probably is one of the negative affects which would would lead to lower efficiency of the AL and LL impeller. In contrast, distribution of Mach number and pressure of the prototype and LA impeller is more uniform, which is beneficial to efficiency. In another words, skin friction loss is another important negative effect to efficiency, which is generated by boundary layers. And the pressure loss coefficient which is resulted from skin friction of solid surfaces can be defined [18] as Appl. Sci. 2018, 8, 1339 8 of 16 lead to lower efficiency of the AL and LL impeller. In contrast, distribution of Mach number and Appl.pressure Sci. 2018 of, 8 the, x FOR prototype PEER REVIEW and LA impeller is more uniform, which is beneficial to efficiency. 8 of 16 In another words, skin friction loss is another important negative effect to efficiency, which is generated by boundary layers. And theω pressure= loss coefficient2 which is resulted from skin friction of SF4(/)CWWL f1 B / d h , (7) solid surfaces can be defined [18] as where, Cf is the skin friction coefficient, W is the averaged2 relative velocity, W1 is the averaged ωSF = 4Cf (W/W1) LB/dh, (7) incidence velocity, LB is the average length of hub and shroud, and dh is the outlet hydraulic diameter.where, C Thef is theaveraged skin frictionrelative coefficient,velocity of theW isfour the impellers averaged is relative very close velocity, to eachW other1 is the as is averaged shown incidence velocity, L is the average length of hub and shroud, and d is the outlet hydraulic diameter. in Figure 7a so thatB skin friction loss is approximately proportionalh to L . Among these four The averaged relative velocity of the four impellers is very close to each other asB is shown in Figure7a impellers, L of LL impeller is shortest and then the skin friction loss of the LL impeller is smallest. so that skinB friction loss is approximately proportional to LB. Among these four impellers, LB of LL impellerFurthermore, is shortest hub and to then shroud the skin loading friction loss, loss ofwhich the LLis impellerproduced is smallest.by secondary flow, can be expressedFurthermore, by the foll hubowed to shroudequation loading [18]. loss, which is produced by secondary flow, can be expressed by the followed equation [18]. ω = 2 Hs (/)/6kBWWm 1 2 , (8) ωHs = (kmBW/W1) /6, (8) where,where, kkmmis is the the blade blade curvature curvature and andB theB hub-to-shroud the hub-to-shroud width. width. It is apparent It is apparent that the that hub-to-shroud the hub-to- shroudwidth ofwidth LL impeller of LL impeller is smallest, is smallest, which meanswhich me weakerans weaker secondary secondary flows and flows less and loading less loading loss. loss. BaseBase on aboveabove analysis, analysis, although although the nonuniformitythe nonuniformity of Mach of numberMach number and pressure and ratiopressure distribution ratio distributioncan be observed can be in observed the LL impeller, in the itsLL performanceimpeller, its canperformance be madeup can by be the made less skinup by friction the less loss skin and frictionloading loss loss. and So, loading as shown loss. in Figure So, as8 shown, there isin a Figure little performance 8, there is a differencelittle performance among four difference impellers among at the fourdesign impellers point. at the design point. InIn addition, addition, the the connection connection form form with with straight straight line line of of LL LL impeller impeller arise arise two two low low Mach Mach number number regionsregions can can be foundfound inin thethe flow flow field field near near the the break break points points because because of the of sharpthe sharp change change of slope, of slope, which whichneeded needed to be concernedto be concerned in this in study.this study. The moreThe more clearly clearly pictures pictures of flow of flow situation situation of LL of impellerLL impeller can canbe seenbe seen in Figurein Figure9. Nevertheless, 9. Nevertheless, this this low low Mach Mach number number region region is small is small compared compared to the to whole the whole flow flowpassage, passage, and and this phenomenonthis phenomenon may may be improved be improved by other by other method method of hub of separation.hub separation.

Relative Mach number

FigureFigure 9. 9. RelativeRelative March March number. number.

AsAs the the machine isis operatedoperated near near the the stall stall point, point, it is it shown is shown in Figure in Figure 10 that 10 the that meridional the meridional relative relativevelocity velocity distribution distribution (Figure (Fig10a)ure and 10a) pressure and pressure coefficient coefficient distribution distribution (Figure 10 (Figureb) of four 10b) impellers of four impellerswith 0.85 with flow rate.0.85 flow It is apparent rate. It is that apparent there is that a high there relative is a high velocity relative domain velocity near thedomain turning near area the of turningshroud area line of LLshroud impeller, line of which LL impeller, is beneficial which to stallis beneficial margin. to stall margin.

Appl. Sci. 2018, 8, 1339 9 of 16 Appl. Sci. 2018, 8, x FOR PEER REVIEW 9 of 16

Appl. Sci.Prototype 2018, 8, x FOR PEER AL REVIEW impeller LA impeller LL impeller Relative velocity 9 of 16

Prototype AL impeller LA impeller LL impeller Relative velocity

(a) Relative velocity

(a) Relative velocity Pressure coefficient Pressure coefficient

(b ) Static pressure coefficient (b) Static pressure coefficient Figure 10. Aerodynamic parameters distribution on meridional plane at the 0.85 flowrate. FigureFigure 10. 10.Aerodynamic Aerodynamic parameters parametersdistribution distribution on on meridional meridional plane plane at atthe the 0.85 0.85 flowrate. ﬂowrate.

4.1.3. Blade to Blade Surface 4.1.3.4.1.3. Blade Blade to Bladeto Blade Surface Surface It is shown in Figure 11 that the relative Mach number distribution for three different sections It isIt shown is shown in Figurein Figure 11 11 that that the the relative relative MachMach number distribution distribution for for three three different different sections sections such suchas span as span wise wise 90% 90% (Figure (Figure 11a 11a), 50%), 50% (Figure (Figure 11b), 11b), andand 10%10% (Figure(Figure 11c) 11c) at at the the design design point. point. For For such as span wise 90% (Figure 11a), 50% (Figure 11b), and 10% (Figure 11c) at the design point. For the the LLthe impeller, LL impeller, the themaximum maximum Mach Mach number number is is about about 0.45, 0.45, whichwhich isis thethe largest largest among among four four impellers, impellers, LL impeller, the maximum Mach number is about 0.45, which is the largest among four impellers, and and theand region the region of high of high Mach Mach number number is isalso also the the biggest biggest asas shown inin thethe Figure Figure 11, 11, which which indicates indicates the region of high Mach number is also the biggest as shown in the Figure 11, which indicates the the biggestthe biggest flowing flowing loss loss at theat the design design point. point. Mean Meanwhile,while, thethe Mach numbernumber near near outlet outlet region region of theof the biggest ﬂowing loss at the design point. Meanwhile, the Mach number near outlet region of the LL LL impellerLL impeller appears appears to be to thebe the highest, highest, which which indicates indicates lower lower static pressurepressure ratio ratio as as is isshown shown in Figurein Figure impeller7b. appears to be the highest, which indicates lower static pressure ratio as is shown in Figure7b. 7b. Prototype AL impeller LA impeller LL impeller Relative Mach number Prototype AL impeller LA impeller LL impeller Relative Mach number

(a) 90% span wise (a) 90% span wise

(b) 50% span wise

Figure 11. Relative Mach number distribution on blade to blade plane at design point. Figure 11. Relative Mach number distribution on blade to blade plane at design point. (c) 10% span wise

Figure 11. Relative Mach number distribution on blade to blade plane at design point. Appl. Sci. 2018, 8, x FOR PEER REVIEW 10 of 16

The relative Mach number distribution at 0.85 design flow rate is shown in Figure 12. The highest Appl.Mach Sci. number2018, 8, 1339can be observed near outlet region in the prototype, which is very different from10 ofthe 16 performance at the design point. This phenomenon means that the flowing situation of the prototype is closing to its stall point, while the LL impeller still has excellent stall tolerance capability. So, the The relativeAppl. Sci. 2018 Mach, 8, x FOR number PEER REVIEW distribution at 0.85 design flow rate is shown in Figure 1210 of. The16 highest LL impeller presents the better pressure ratio at the low flow rate than the prototype, which can also Mach number can be observed near outlet region in the prototype, which is very different from the be obtained inThe Figure relative 6. Mach number distribution at 0.85 design flow rate is shown in Figure 12. The highest performanceMach at number the design can be point. observed This near phenomenon outlet region in means the prototype, that the which flowing is very situation different from of the the prototype performance at the design point. This phenomenon means that the flowing situation of the prototype is closingPrototype to its stall point, AL impeller while the LL impeller LA impeller still has excellent LL impeller stall tolerance Relative capability. Mach number So, the LL impeller presentsis closing theto its better stall point, pressure while the ratio LL atimpeller the low still flowhas excellent rate than stall thetolerance prototype, capability. which So, the can also be LL impeller presents the better pressure ratio at the low flow rate than the prototype, which can also obtained inbe Figureobtained6. in Figure 6.

Prototype AL impeller LA impeller LL impeller Relative Mach number

(a) 90% span wise

(b) 50% span wise (b) 50% span wise

(c)(c 10%) 10% spanspan wise wise Figure 12. Relative Mach number distribution on blade to blade plane at 0.85 flowrate. Figure 12. Relative Mach number distribution on blade to blade plane at 0.85 flowrate.flowrate. 4.2. Full Passage 4.2. Full Passage 4.2.1. Overall Performance 4.2.1. Overall Performance The overall performance of the LL impeller with full passage model is shown in Figure 13. In this figure, the experimental data referred to is from Reference [19]. The calculation result of the full The overallpassage performanceperformancemodel can be matched of of the the LL withLL impeller impellerexperiments with with ve fullry full well, passage passage while modelthe model performance is shownis shown of in the Figure in single Figure 13. In13. this In thisfigure, figure, thepassage experimental the experimental model is data different referreddata from referred tothat is of from tothe is experi Reference fromment. Reference In [19 the]. Thesingle [19]. calculation passage The calculation model, result the ofvolute result the fullis of passagethe full ignored so that flowing loss in volute is not considered. passagemodel can model be matched can be withmatched experiments with experiments very well, while very thewell, performance while the ofperformance the single passage of the modelsingle passageis different model from is thatdifferent of the from experiment. that whole of passagethe In theexperi model singlement. passage In the model,single passage the volute whole model, passage is ignored model the volute so that is Experiments[19] 1.44 Experiments[19] Single passage model ignoredflowing lossso that0.92 in voluteflowing is loss not considered.in volute Single is not passage considered. model

0.90 1.42

0.88 whole passage model whole passage model Experiments[19] Experiments[19] 1.401.44 0.86 Single passage model 0.92 Single passage model 0.84 1.38

0.90 Efficiency 0.82 1.42 Pressure ratio

0.88 0.80 1.36

0.78 0.86 1.40

0.76 1.34 0.84 0.7 0.8 0.9 1.0 1.1 1.2 0.7 0.8 0.9 1.0 1.1 1.2 Normalized mass flow rate(Q/Qd) 1.38 Normalized mass flow rate (Q/Qd) Efficiency 0.82 (a) Efficiency verses flow rate Pressure ratio (b) Pressure ratio verses flow rate

0.80 Figure 13. Performance verses1.36 flow rate.

0.78

0.76 1.34 0.7 0.8 0.9 1.0 1.1 1.2 0.7 0.8 0.9 1.0 1.1 1.2 Normalized mass flow rate(Q/Qd) Normalized mass flow rate (Q/Qd) (a) Efficiency verses flow rate (b) Pressure ratio verses flow rate

Figure 13. Performance verses flow flow rate. Appl. Sci. 2018, 8, 1339 11 of 16 Appl. Sci. 2018, 8, x FOR PEER REVIEW 11 of 16 Appl. Sci. 2018, 8, x FOR PEER REVIEW 11 of 16 ItIt is is shown shown in in Figure Figure 14 14 thatthat the the numerical numerical result result comparison comparison of of Mach Mach number number and and pressure pressure coefficientcoefficientIt distribution distributionis shown in between Figure between 14 full fullthat passage passage the numerical (Fig (Figureure result14a) 14a) and andcomparison single single passage passage of Mach (Figure (Figure number 14b) 14 andb) at at pressurethe the designdesigncoefficient point. point. It It isdistribution is apparent apparent that thatbetween the the flow flow full pattern patternpassage of of real(Fig real urecompressor compressor 14a) and is is singleunsymmetrical unsymmetrical passage (Figurebecause because 14b)of of the the at the unsymmetricalunsymmetricaldesign point. geometrical geometrical It is apparent structure structure that theof of the theflow volute. volute. pattern of real compressor is unsymmetrical because of the unsymmetrical geometrical structure of the volute. Relative Mach number Relative Mach number

Pressure coefficient Pressure coefficient

(a) Whole flow passage (b) Single impeller flow passage (a) Whole flow passage (b) Single impeller flow passage Figure 14. Blade to blade performance comparison at design point, 50% span wise. Figure 14. Blade to blade performance comparison at design point, 50% span wise. Figure 14. Blade to blade performance comparison at design point, 50% span wise. The circumferential flow situation of mid-surface can be seen in Figure 15. The absolute Mach numberThe (FigureThe circumferential circumferential 15a) and pressure flow flow situation distribution situation of mid-surface of (F mid-surfaceigure 15b) can are becan evidently seen be seen in Figure inasymmetric Figure 15. The15. throughout The absolute absolute Mach the Mach compressornumbernumber (Figure because (Figure 15a) of 15a) and asymmetric and pressure pressure structure distribution distribution of volute (Figure (F.igure There 15b) 15b)are is an evidentlyare obvious evidently asymmetrichigh asymmetric Mach number throughout throughout region the the incompressor thecompressor impeller because near because the of asymmetrictongue of asymmetric of volute, structure structure and ofthe volute. staticof volute pressure There. There isan of is obviousthis an obviousregion high is high Machalso Mach relatively number number regionhigh. region Itin can thein be impellerthe inferred impeller near that near the the tongue thetongue tongue of of volute, volute of volute, andhas andsignificant the staticthe static pressure impact pressure in of the this of nearbythis region region flow. is also is also relatively relatively high. high. It canIt becan inferred be inferred that that the tonguethe tongue of volute of volute has significanthas significant impact impact in the in nearby the nearby flow. flow.

(a) Absolute Mach number (b) Static pressure coefficient (a) Absolute Mach number (b) Static pressure coefficient Figure 15. Performance of whole flow passage at design point. FigureFigure 15. Performance 15. Performance of whole of whole flow flow passage passage at design at design point. point. 4.2.2. Unsteady Results 4.2.2. Unsteady Results 4.2.2.All Unsteady of the above Results studies are based on steady flow field, but, the impeller is exposed to All of the above studies are based on steady flow field, but, the impeller is exposed to downstreamAll of the circumferential above studies areunsteady based onflow, steady which flow resulted field, but, in theblade impeller vibratio isns exposed and auxiliary to downstream noise downstream circumferential unsteady flow, which resulted in blade vibrations and auxiliary noise [20].circumferential unsteady flow, which resulted in blade vibrations and auxiliary noise [20]. [20]. TheThe acoustic acoustic Strouhal Strouhal number number is is employed employed to to characterize characterize unsteady unsteady interaction interaction of of impeller impeller and and The acoustic Strouhal number is employed to characterize unsteady interaction of impeller and volutevolute of of compressible compressible flows. flows. This This can can be be defined defined as as follows: follows: volute of compressible flows. This can be defined as follows: fL St = f L St = ,, fL (9) (9) StCC = , (9) C where,where, ff is is thethe rotationalrotational frequency, CCthe the speed speed of of soundsound estimatedestimated with with the the inlet inlet temperature. temperature. where, f is the rotational frequency, C the speed of sound estimated with the inlet temperature. StSt representsrepresents temporal relationship between ro rotationtation speed speed of of impeller impeller and and perturbation perturbation wave wave propagationSt represents of flow temporal in the impeller. relationship Unsteady between effects rotation can be speed neglected of impeller when andSt  perturbation0.1 and the wave relativelypropagation accurate of results flow canin the be impeller.evaluated Unsteady by steady effects calculations. can be While neglected St > when0.1, moreSt  accurate0.1 and the relatively accurate results can be evaluated by steady calculations. While St > 0.1, more accurate Appl. Sci. 2018, 8, 1339 12 of 16 Appl. Sci. 2018, 8, x FOR PEER REVIEW 12 of 16 propagationresults can be of obtained flow in thethrough impeller. unsteady Unsteady flow calculations effects can be[21]. neglected In this case, when StSt is about0.1 and 0.12 the at relativelydesign point. accurate It implies results that can the be propagation evaluated byof pressu steadyre calculations. wave is faster While than Stthe> rotation0.1, more speed accurate of the resultsimpeller. can Therefore, be obtained the throughunsteady unsteady numerical flow investigation, calculations which [21]. Inis thisfocused case, onSt isthe about response 0.12 atof designpressure point. distortions It implies imposed that theby asymmetric propagation geomet of pressurery of volute, waveis is fasternecessary than to the be rotation conducted. speed of the impeller.Since time-accurate Therefore, the simulation unsteady of numerical the unstea investigation,dy phenomenon, which rotational is focused speed on the and response angular of pressuredisplacement distortions between imposed two successive by asymmetric computations geometry should of volute, be considered is necessary into to be the conducted. numerical time step.Since The dual-time time-accurate step simulation(DTS) method of the was unsteady adopted phenomenon, to improve th rotationale time marching speed andin unsteady angular displacementcalculation because between the two adopting successive of full computations passage mesh should and bethe considered highly quality into themesh numerical in this study. timestep. The Theunsteady dual-time Rotor/Stator step (DTS) interface method was was adoptedset by doma to improvein scaling the timemethod marching [22]. The in unsteady number calculationof angular becausepositions the is set adopting to be 20 of in full one passage single passage, mesh and so thethere highly are total quality of 240 mesh angula in thisr positions. study.The The unsteadytime step Rotor/StatorΔt can be expressed interface as was equation set by follows: domain scaling method [22]. The number of angular positions is set to be 20 in one single passage, so there are total of 240 angular positions. The time step ∆t can be 2π expressed as equation follows: Δ=t , (10) ω ⋅⋅2π ∆t = Nperiods NOFROT (10) ω · Nperiods · NOFROT where, ω is the rotor rotation, Nperiods is the number of periodicities and NOFROT is the number where, ω is the rotor rotation, Nperiods is the number of periodicities− and5 NOFROT is the number of angular positions, so, in this study the time step was Δ=t 4.5 × 10 s , and the steady numerical of angular positions, so, in this study the time step was ∆t = 4.5 × 10−5s, and the steady numerical simulation result is set to be the initial condition of unsteady numerical calculation in the first period. simulation result is set to be the initial condition of unsteady numerical calculation in the first period. The positions of the seven probes are shown in Figure 16, of which six probes are located at the The positions of the seven probes are shown in Figure 16, of which six probes are located at the outlet of impeller and one at the tongue. It is shown in Figure 17 that shows the nondimensionalized outlet of impeller and one at the tongue. It is shown in Figure 17 that shows the nondimensionalized static pressure variation of six probes at different locations, respectively. The horizontal ordinate is static pressure variation of six probes at different locations, respectively. The horizontal ordinate is Δ= × −5 thethe physicalphysical timetime whichwhich meansmeans thethe rotorrotor needneed unitaryunitary timetime stepstep ((∆tt= 4.5 × 1010−5 ss)) toto revolverevolve oneone angularangular position,position, so there are total of 240 ∆Δttbecause because of of 240 240 angular angular positions. positions. ItIt cancan bebe seenseen thatthat thethe flowflow fieldfield presentedpresented aa periodicperiodic fluctuationfluctuation andand thethe shapeshape ofof curvescurves are different duedue toto the asymmetric configurationconfiguration ofof volute.volute. Meanwhile, phase shift betweenbetween different probe positions is also observed. ItIt isis duedue toto thethe propagationpropagation ofof pressurepressure perturbationperturbation fromfrom oneone bladeblade channelchannel to to the the next. next.

FigureFigure 16.16. PositionPosition ofof probe.probe.

The oscillation of nondimensionalized static pressure of probe 7 at tongue position in a period can be seen in Figure 18. The amplitude of pressure oscillation of tongue is smaller than those of impeller outlet positions, but the frequency of pressure oscillation is bigger. Since the amplitude of pressure oscillation is small, only about 1.5%, the steady numerical simulation result at the tongue position is accurate enough. Appl. Sci. 2018, 8, x FOR PEER REVIEW 13 of 16

probe 1 1.06 Phase shift probe 2 probe 3 probe 4 1.04 probe 5 probe 6

Appl. Sci. 2018, 8, xAppl. FOR Sci. PEER2018, 8, 1339REVIEW1.02 13 of 16 13 of 16

1.00 probe 1 1.06 Phase shift probe 2 probe 3 0.98 probe 4 Nondimesionalized pressure Nondimesionalized 1.04 probe 5 probe 6 0.96

1.02 0Δt 50Δt 100Δt 150Δt 200Δt 250Δt Physical time(s) 1.00 Figure 17. Nodimensionalized pressure verses the time of six probes.

0.98 The oscillation of nondimensionalized pressure Nondimesionalized static pressure of probe 7 at tongue position in a period can be seen in Figure 18. The0.96 amplitude of pressure oscillation of tongue is smaller than those of impeller outlet positions, but the frequency of pressure oscillation is bigger. Since the amplitude of 0Δt 50Δt 100Δt 150Δt 200Δt 250Δt pressure oscillation is small, only about 1.5%, Physicalthe steady time(s) numerical simulation result at the tongue position is accurate enough. Figure 17.Figure Nodimensionalized 17. Nodimensionalized pressure pressure verses verses the time the of time six probes. of six probes.

probe 7 The oscillation of nondimensionalized static pressure of probe 7 at tongue position in a period can be seen in Figure 18. The1.015 amplitude of pressure oscillation of tongue is smaller than those of impeller outlet positions, but the frequency of pressure oscillation is bigger. Since the amplitude of pressure oscillation is small,1.010 only about 1.5%, the steady numerical simulation result at the tongue position is accurate enough.

1.005 probe 7

1.000 1.015 Nondimensionalized pressure Nondimensionalized 0.995 1.010

0Δt 50Δt 100Δt 150Δt 200Δt 250 Δt 1.005 Physical time(s) Figure 18.Figure Nodimensionalized 18. Nodimensionalized pressure pressure verses verses the step the of probestep 7.of probe 7. 1.000 It can be seen in Figure 19 that static pressure distribution at different time steps of 50% radial It can be seen in Figure 19 that static pressure distribution at different time steps of 50% radial height near hub pressure Nondimensionalized in one channel period. When the relative position between impeller and volute is the height near hubsame in asone that channel of steady0.995 simulation, period. theWhent is adopted the relative as 0. Transformation position of between static pressure impeller distribution and volute is the same as that ofindicates steady unsteady simulation, characteristics, the t is but adopted the inﬂuence as of 0. which Transformation is not obviously. Therefore,of static the pressure steady distribution numerical simulation result can0Δt be used 50Δ fort investigating 100Δt circumferential150Δt 200Δt asymmetric 250 Δt ﬂow pattern in indicates unsteady characteristics, but the influence of which is not obviously. Therefore, the steady this study. Physical time(s) numerical simulation result can be used for investigating circumferential asymmetric flow pattern in Figure 18. Nodimensionalized pressure verses the step of probe 7. this study. It can be seen in Figure 19 that static pressure distribution at different time steps of 50% radial height near hub in one channel period. When the relative position between impeller and volute is the same as that of steady simulation, the t is adopted as 0. Transformation of static pressure distribution indicates unsteady characteristics, but the influence of which is not obviously. Therefore, the steady numerical simulation result can be used for investigating circumferential asymmetric flow pattern in this study.

Appl. Sci. 2018, 8, 1339 14 of 16 Appl. Sci. 2018, 8, x FOR PEER REVIEW 14 of 16

Pressure coefficient

(a) tTDTS= 0/6 (b) tTDTS=1/6 (c) tTDTS= 2/6 Pressure coefficient

(d) tTDTS= 3/6 (e) tTDTS= 4/6 (f) tTDTS= 5/6

FigureFigure 19. 19.Dimensionless Dimensionless static static pressure pressure coefficient coefficient distribution distribution at different at different time steps.time steps. DTS: dual-timeDTS: dual- step. time step. 5. Discussions 5. Discussions As mentioned above, the performance of compressor can be influenced significantly by the shape As mentioned above, the performance of compressor can be influenced significantly by the of meridional contours. The simplified hub design method is based on the selection of the break points. shape of meridional contours. The simplified hub design method is based on the selection of the break In this study, the break points are selected when the slope is discontinuous at the points. However, points. In this study, the break points are selected when the slope is discontinuous at the points. there may be another method to screen the break points, by which more optimized design would be However, there may be another method to screen the break points, by which more optimized design achieved. We plan to discuss in near future research. would be achieved. We plan to discuss in near future research. Straight lines are applied to describe the hub contours, by which the hub shape is changed, and Straight lines are applied to describe the hub contours, by which the hub shape is changed, and the area of flow passage is narrowed. It is due to the narrowed passage that the velocity is increased, the area of flow passage is narrowed. It is due to the narrowed passage that the velocity is increased, which is beneficial to the aerodynamic performance sometime especially when machine is operated which is beneficial to the aerodynamic performance sometime especially when machine is operated close to the stall point. However, further research is needed on how to evaluate contribution of the close to the stall point. However, further research is needed on how to evaluate contribution of the narrowed passage to the stall margin. narrowed passage to the stall margin. In this study, the working medium is water vapor and the rotation speed relatively low so that In this study, the working medium is water vapor and the rotation speed relatively low so that the compressor performance is stable, and the efficiency and pressure ratio are not changed obviously the compressor performance is stable, and the efficiency and pressure ratio are not changed obviously with the flow rate. However, for another kinds of compressor, the simplified hub contours would give with the flow rate. However, for another kinds of compressor, the simplified hub contours would rise to violent change on performance. This is a concern for future research. give rise to violent change on performance. This is a concern for future research. Additionally, it is found in all cases that the region of large Mach number is around the leading Additionally, it is found in all cases that the region of large Mach number is around the leading edge of the splitters. This means that the location of the splitters can also influence the Mach number edge of the splitters. This means that the location of the splitters can also influence the Mach number distribution. It has been proved that optimizing location of the splitter can improve the performance distribution. It has been proved that optimizing location of the splitter can improve the performance of centrifugal compressor [23], so the splitter design should be considered in the future optimization of centrifugal compressor [23], so the splitter design should be considered in the future optimization of impeller. of impeller. 6. Conclusions 6. Conclusions In order to simplify meridional configuration, three impellers are designed with innovative shape. BasedIn onorder the Computationalto simplify meridional Fluid Dynamics configuration, (CFD) method,three impellers detail analysis are designed of steady with and innovative unsteady shape.flow field Based has on been the Computational carried out with Fluid single-passage-model Dynamics (CFD) method, and full-passage-model detail analysis of respectively.steady and unsteadyFurthermore, flow the field experiment has been results carried are used out towith evaluate single-passage-model the accuracy of CFD and results. full-passage-model The conclusions respectively.can be drawn Furthermore, as following: the experiment results are used to evaluate the accuracy of CFD results. The conclusions can be drawn as following: • The processing time and manufacturing cost are reduced because the hub is described by the straight line for the optimized impeller, LL impeller. Moreover, the hollow geometry in the disk may also be beneficial to the rotor dynamic design and bearing design. Appl. Sci. 2018, 8, 1339 15 of 16

• The processing time and manufacturing cost are reduced because the hub is described by the straight line for the optimized impeller, LL impeller. Moreover, the hollow geometry in the disk may also be beneficial to the rotor dynamic design and bearing design. • Within the operating range, the prototype impeller has stable performance. Nevertheless, its operating range cannot fully match the industrial requirement. Meanwhile, the simplified impeller, LL impeller, is improved with excellent stall margin as well as its efficiency and pressure ratio are decreased little. • The calculation result of the full passage model is matched with experiments very well. So, in order to obtain comprehensive performance of a centrifugal compressor, full passage model with volute is necessary to be considered. • In this case, unsteady calculation is conducted due to St 0.12, but the unsteady characteristics of the steam compressor is not obvious. Meanwhile, the amplitude of pressure oscillation around volute tongue is only about 1.5%. Thus, for this case, the steady numerical simulation result is accurate enough to investigate asymmetric circumferential flow pattern.

Author Contributions: Conceptualization, B.Y.; Investigation, H.X.; Software, X.L. and M.S.; Resources, C.G.; Writing-Review & Editing, H.X. Funding: This research received no external funding. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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