Improving Centrifugal Compressor Performance by Optimizing the Design of Impellers Using Genetic Algorithm and Computational Fluid Dynamics Methods

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Article Improving Centrifugal Compressor Performance by Optimizing the Design of Impellers Using Genetic Algorithm and Computational Fluid Dynamics Methods

Mohammad Omidi 1 , Shu-Jie Liu 1,*, Soheil Mohtaram 2, Hui-Tian Lu 3 and Hong-Chao Zhang 1,4

1 School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, China; [email protected] (M.O.); [email protected] (Z.H.-C.) 2 Institute of Soft Matter Mechanics, College of Mechanics and Materials, Hohai University, Nanjing 210098, China; [email protected] 3 Department of Construction & Operations Management, South Dakota State University, Brookings, SD 57007, USA; [email protected] 4 Department of Industrial Engineering, Texas Tech University, Lubbock, TX 79409, USA * Correspondence: [email protected]; Tel.: +86-411-84709302

Received: 2 September 2019; Accepted: 27 September 2019; Published: 30 September 2019

Abstract: It has always been important to study the development and improvement of the design of turbomachines, owing to the numerous uses of turbomachines and their high energy consumption. Accordingly, optimizing turbomachine performance is crucial for sustainable development. The design of impellers significantly affects the performance of centrifugal compressors. Numerous models and design methods proposed for this subject area, however, old and based on the 1D scheme. The present article developed a hybrid optimization model based on genetic algorithms (GA) and a 3D simulation of compressors to examine the certain parameters such as blade angle at leading and trailing edges and the starting point of splitter blades. New impeller design is proposed to optimize the base compressor. The contribution of this paper includes the automatic creation of generations for achieving the optimal design and designing splitter blades using a novel method. The present study concludes with presenting a new, more efficient, and stable design.

Keywords: genetic algorithm (GA); optimization; computational ﬂuid dynamics (CFD); centrifugal compressor

1. Introduction

Greenhouse gases such as carbon dioxide (CO2) are the main cause of climate change. Decreasing these emissions to prevent global warming is of crucial importance. Simultaneously the energy industry, traffic, and numerous forms of transportation all emit significant amounts of CO2.[1]. Turbomachines, including centrifugal compressors and pumps, consume a huge amount of energy in the world, both directly and indirectly [2,3]. Turbomachinery is a part of everyday life [4]. They are of central importance in various ways such as aeronautics, petrochemical processing, generation of power, refrigeration, etc. They contribute to compressors, turbochargers, pumps, turbines, and other integral equipment [4]. When applied to a wide variety of uses, even miniscule changes in efficiency and design can yield massive benefits [5]. Sustainable development will, to a certain degree, depend upon the performance improvement of turbomachinery.

Sustainability 2019, 11, 5409; doi:10.3390/su11195409 www.mdpi.com/journal/sustainability Sustainability 2019, 11, 5409 2 of 18

One of the most important problems with using these machines is their damping and extremely high rates of energy loss compared to other types of machines. However, due to the fluidity of the output of these machines, as well as their relatively uncomplicated design and process system, they are still far superior to other types of compressors used. The impeller is the most important part of a turbomachine, as it plays a critical role in fluid processing, and it has therefore constantly been redesigned, optimized, and restudied over time. However, centrifugal impellers have many limitations that still need to be improved upon with redesign. Blades on the compressor impeller have always had the most significant impact on the efficiency and performance of these machine parts. Many available resources have adopted different approaches to design impellers in centrifugal compressors [6,7]. An impeller is the rotary component of centrifugal compressors that consists of blades, which are geometrically complex due to their profile, and their flow pattern is 3D with secondary flows [8]. Given the different design parameters and flow aspects, studying impellers in centrifugal compressors is crucial. Making efforts to optimize the design of impeller as a key component is crucial given that the performance of compressors highly depends on its design [9]. Research suggests that impeller contribution to losses is significant compared to other components of a centrifugal compressor [7]. Proposing efficiency enhancement methods is therefore of great importance in this area. The method proposed by Swine to change the impeller design [10,11], namely trimming, begins with a scratch design of impeller and proceeds to make it more delicate. This process can affect the boundaries of impellers in different directions. The direction of correction in their study was axial, radial, and stream-wise. [12] optimized compressors by redefining the curve at the hub and shroud and changing control points in the Bezier polynomial, achieving a 0.6% improvement in the pressure ratio and 1.4% improvement in efficiency. Breaking the shape and number of impellers constitutes the general secondary methods for optimizing impellers. According to this method, [13] investigated the effect of inserting two splitter blades between the main blades rather than relying on the typical setup, and could increase the mass flow rate and even efficiency and the pressure ratio. Moreover, [14] conducted an experimental study on this subject. Improvements in the performance of compressors were also reported in the literature [15], by experimentally testing impellers. [16] proposed an optimization method by changing the shape of blades, while considering the instability margin of the compressor, and found the inlet angle of the impeller to exert significant effects on the compressor efficiency. Given that the outer radius and width of the outlet contribute to instability, the shape of blades remained unchanged. [17] argued that the leading edge of sonic compressors could create shock waves when placed in an area greater than Mach one, negatively affecting splitter blades. This problem was solved by moving the starting point of the splitter forward and out of this area. [18] also proposed an optimization method for enhancing the efficiency of centrifugal compressors, which involved using the same profile for the primary and splitter blades and changing the initial profile using the Bezier polynomial points. The results suggested an efficiency increase of about 2.5%. Moreover, [19] specified certain parameters for the objective function, including pressure ratio, efficiency and thrust, and changed the impeller profile from the hub to shroud, resulting in incredible improvements, including an efficiency increase of 4.5% and a pressure ratio increase of 16%. Investigating the effect of exit pressure pulsation on the performance and stability limit of a turbocharger centrifugal compressor, [20] showed that the presence of a volume in the system exerts the most significant effect on the surge margin of the compressor under unsteady conditions. Optimizing the aerodynamic design of the impellers of a centrifugal compressor using an inverse method based on the meridional viscous flow analysis [21] resulted in performance improvements and suppression of flow separations on the suction surfaces in the optimal design cases. The present optimization scheme specifies the changes in parameters using the computational fluid dynamics (CFD) data that correct the differences for the next steps. CFD has been widely used in the compressor designs, and there are many design considerations that need to be addressed during the Sustainability 2019, 11, 5409 3 of 18 designing process [22,23]. From a mathematical perspective, this scheme determines the direction and value of the gradient of parameters. Artificial neural network [18] and GA were used for this analysis. GA uses mechanisms such as mutation and cross-over to produce new generations of compressors [24]. This algorithm produces different versions of a compressor in different generations, and decides on terminating certain generations and refining others based on simulation results. Due to the secondary flows in the impellers of centrifugal compressor splitter blades, the situation is not the same as that of the main blades. The flow does not match with splitter blades and this leads to performance loss in the compressors. To mitigate this loss, compressor blades should be redesigned. In this project, the changes in geometry of blade flow regimes will be analyzed. If the target is a specific compressor, this modification is limited to the impellers; otherwise, it may be necessary to change other parts, as well. The same constraints used in previous studies with the same profile for the main and splitter blades were not used in the present research. A wider range of parameters was therefore explored when optimizing the compressor design. Two different base methods are generally used for compressor optimization. The trimming method makes small changes in the design parameters of impellers and monitors the effect of these changes on the overall performance of compressors while focusing on parameters such as Bezier points. This method is usually based on a constrained range of parameters, and is efficient in terms of computational burden, although its results are user-dependent given the need for a manual search in the computational domain of optimization. The second method investigates major changes made in the blade shape and number and the beginning and end points of splitters. This method usually automatically examines parameters and a wide range of designs including a higher number of parameters compared to the trimming method. An optimization algorithm is integrated into this method to search in the domain of solutions and show the direction of steps towards an optimized system. In addition, given the mathematical algorithm behind optimizations, the results are unpredictable and the computational burden is heavier than that of the first method.

2. Optimization Procedure Genetic algorithm is a method for optimizing a function called the objective or fitness function on a domain. The value of the objective function is calculated at randomly selected points of the domain. Each set of points form a generation, and the first generation is randomly selected from the domain. The best members of every generation with the highest objective function values can be included in the next generation. Generation members are therefore gradually improved, and this process continues until an arbitrary condition stops the algorithm. Optimization begins with current blades of a compressor and repeatedly alters the impeller and checks the performance to achieve a better design. A code was therefore developed and an automatic process was designed. This process begins with the base compressor and is slightly modified by GA. The performance of this altered compressor is examined by simulating the flow using CFD methods, which guides GA to find the optimization direction and create a new generation. At each step, GA tests certain pre-defined geometrical design parameters of the compressor for the steps ahead. This chain of actions leads to creating different generations of the compressor. Performance is improved through generations until GA reaches the terminating point. The code helps manage this process by connecting GA to the CFD code for conducting simulations and transmitting data between the two algorithms. Although this method suits a multi-parameter system such as a compressor, flow simulations requiring many calculations make the whole process large, costly, and very time consuming in a way that the optimization approximately takes six days of the CPU time. The number of iterations is limited in CFD modelling depending on the accuracy needed and the amount of calculation allowed. However, the process termination is not enforced in GA as the algorithm automatically stops the calculations if it finds out that no further improvements in performance can be achieved. Sustainability 2019, 11, 5409 4 of 18

Figure1 shows the e fficiency optimization process of the best efficiency point (BEP) in the optimized compressor as well as some generations. The minor improvement observed in one generation is due to the similarity of all the designs belonging to that generation; nevertheless, mutation, as a GA tool, Sustainability 2019, 11, x FOR PEER REVIEW 4 of 18 createsSustainability a new 2019 totally, 11, x FOR diff PEERerent REVIEW generation between two generations. 4 of 18

Figure 1. The efficiency (%) optimization process. Figure 1. The efficiency (%) optimization process. Variations in blade profiles should be expressed as multiple interpolations, which can be modified Variations in blade profiles should be expressed as multiple interpolations, which can be by changing control points used by this optimization method. To create these interpolations, a 3D modified by changing control points used by thisthis optimizationoptimization method.method. ToTo createcreate thesethese model of the impeller was developed in which the impeller was divided into separate parts, and each interpolations,interpolations, aa 3D3D modelmodel ofof thethe impellerimpeller waswas developeddeveloped inin whichwhich thethe impellerimpeller waswas divideddivided intointo part was broken into points and estimated with an appropriate interpolation. The difficulty of grid separate parts, and each part was broken into pointsts andand estimatedestimated withwith anan appropriateappropriate interpolation.interpolation. generationThe difficulty is that of grid it must generation suit different is that designs it must of suit compressors different anddesigns impellers of compressors with different and geometries,impellers whichwith different need special geometries, treatment. which Figure need2 specialshows treatment. the 3D model Figure of the2 shows impeller. the 3D model of the impeller.

Figure 2. Three-dimensional (3D)/Meshing model of impeller. Figure 2. Three-dimensional (3D)/Meshing model of impeller. Different designs of each compressor are analyzed by simulating the flow field through all of the machinesDifferent using designs a commercial of each code. compressor The BEP are of theanalyzed base compressor byby simulatingsimulating makes thethe up flowflow the operatingfieldfield throughthrough conditions allall ofof forthethe this machinesmachines simulation, usingusing and aa commercialcommercial the comparisons code.code. areTheThe therefore BEPBEP of the valid base for compressor this point. makes up the operating conditionsThe design for this loop simulation, for the impeller and the formingcomparisons the optimizationare therefore valid method for basedthis point. on GA analyzes the parametersThe design of flow loop field, for including the impeller pressure forming ratio, the effi optimizationciency and Y +method, as the based inputs on into GA the analyzes optimization the code,parameters to create of new flow designs field, [including25]. pressure ratio,tio, efficiencyefficiency andand Y+,Y+, asas thethe inputsinputs intointo thethe optimization code, to create new designs [25]. GA seeks to minimize or maximize the objective function as a combination of performance parameters of the compressor, including pressure ratiotio andand efficiency.efficiency. TheThe weightweight ofof eacheach parameterparameter inin thisthis functionfunction dependsdepends onon thethe designdesign objectivesobjectives.. GivenGiven thatthat pressurepressure ratioratio cancan bebe increasedincreased usingusing simpler methods such as increasing the compressor diameter compared to efficiency improvement Sustainability 2019, 11, 5409 5 of 18

GA seeks to minimize or maximize the objective function as a combination of performance parameters of the compressor, including pressure ratio and efficiency. The weight of each parameter in this function depends on the design objectives. Given that pressure ratio can be increased using simpler methods such as increasing the compressor diameter compared to efficiency improvement methods, maximizingSustainability 2019 effi, 11ciency, x FORis PEER more REVIEW emphasized in literature when optimizing centrifugal compressors.5 of 18 Only one or a number of operating points can be considered in optimizations. Although the second methodmethods, cited maximizing is not very efficiency popular, itis improves more emphasized the performance in literature of a compressor when optimizing compared tocentrifugal the base designcompressors. in thewhole Only one range or ofa number operation of operating conditions poin ratherts can than be in considered a single operating in optimizations. point. Equation Although (1) showsthe second the mass method flow cited averaged is not everyfficiency: popular, it improves the performance of a compressor compared

to the base design in the whole range of operation co. nditions rather than in a single operating point. R m2 . Equation (1) shows the mass flow averaged efficiency:. η dm m1 φ = 1 . . (1) − m m 2 𝜂1 𝑑𝑚 𝜙=1− − (1) 𝑚 −𝑚 . where φ is the objective function, η is the efficiency and m represents the mass flow rate of the compressorwhere 𝜙 is andthe objective the indices function, show the 𝜂 maximumis the efficiency and minimum and 𝑚 represents operating the points mass of flow the compressor. rate of the Thiscompressor function and indicates the indices that the show parameter the maximum that will and be optimized minimum and operating is a mass points flow averagedof the compressor. efficiency inThis overall function working indicates points that of the the compressor parameter in that one will rotational be optimized speed. and is a mass flow averaged efficiencyVariables in overall should working be determined points of in the the compressor optimization in toone specify rotational the degree speed.of freedom associated withVariables the optimization should be parameters. determined The in the higher optimizati the numberon to specify of parameters the degree selected, of freedom the longerassociated the calculationwith the optimization duration and parameters. the heavier The the higher data processing the number load. of Moreover,parameters certain selected, variables the longer that didthe notcalculation significantly duration contribute and the to heavier the results the weredata processing selected at load. the following Moreover, points certain for variables the optimization, that did Figurenot significantly3 shows the contribute schematic to of the the results following were optimization selected at the variables: following points for the optimization, Figure 3 shows the schematic of the following optimization variables: The initial point of the blades in the hub profile • • the initialThe initial point ofpoint the of blades the blades in the in mid-span the hub profileprofile • • the initialthe initial point point of the of blades the blades in the in tip the profile mid-span profile • • the initial point of the blades in the tip profile peripheral angle specifying the splitter position versus the main blades • • peripheral angle specifying the splitter position versus the main blades

Figure 3. Schematic of the optimization variables. Figure 3. Schematic of the optimization variables. Certain constraints should be applied on these parameters to design a real optimized compressor, otherwiseCertain the constraints optimization should process be will applied create on non-physical these parameters designs. to The design initial pointa real of optimized blades is limitedcompressor, between otherwise the initial the optimization and ending ofprocess the main will create blades non-physical and the peripheral designs. angle The initial between point two of sequentialblades is limited blades. between the initial and ending of the main blades and the peripheral angle between two sequentialEquation (2) blades. presents the mathematical model of the problem. Equation (2) presents the mathematical model of the problem. ObjectiveObjective function function(Φ()Φ=) f= (fa (,ab, ,bc,, cd, )d) (2)(2) Given the method selected for the optimization, a scheme is designed for achieving the goal. The optimization method involves an iterative process, and the optimization algorithm includes several steps as follows: (1) Making curves for blades (2) Developing 3D models of the new impeller (3) Creating a grid for the new impeller (4) Simulating the flow field of the impeller Sustainability 2019, 11, 5409 6 of 18

Given the method selected for the optimization, a scheme is designed for achieving the goal. The optimization method involves an iterative process, and the optimization algorithm includes several steps as follows:

(1) Making curves for blades (2) Developing 3D models of the new impeller

Sustainability(3) Creating 2019, 11 a, grid x FOR for PEER the REVIEW new impeller 6 of 18 (4) Simulating the flow field of the impeller (5)(5) AnalyzingAnalyzing the the flow flow field field and an proposingd proposing new new curves curves based based on flow on simulationsflow simulations (6)(6) RepeatingRepeating the the process process

2.1.2.1. Step Step 1 1 ForFor optimization optimization of of the the blade, blade, its its geometry geometry shou shouldld be expressed usingusing interpolations,interpolations, which which can can bebe modified modiﬁed byby changing changing control contro pointsl points used byused the optimizationby the optimization method to createmethod these to interpolations. create these interpolations.The 3D model The of the 3D impeller model of described the impeller earlier described divides earlier the impeller divides into the separate impeller parts, into andseparate each parts, part andis broken each part into is certain broken points into certain and estimated points and with estimated an appropriate with an interpolation. appropriate interpolation.

2.2.2.2. Step Step 2 2 The 3D model of the impeller was developed in Bladegen, which uses a file specifying all the The 3D model of the impeller was developed in Bladegen, which uses a file specifying all the impeller details. The optimization method alters this file to change the impeller geometry. Bladegen is impeller details. The optimization method alters this file to change the impeller geometry. Bladegen a professional software used for designing turbo machines. It has special sections for radial impellers, is a professional software used for designing turbo machines. It has special sections for radial axial turbines and compressors, IGV, vanned diffusers, etc. A design of profiles, blades, and flow impellers, axial turbines and compressors, IGV, vanned diffusers, etc. A design of profiles, blades, channels in the compressor is developed with this software (Figure4). and flow channels in the compressor is developed with this software (Figure 4).

Figure 4. A design of profiles, blades, and flow channels in the compressor is developed with the Figure 4. A design of profiles, blades, and flow channels in the compressor is developed with the Bladegen software. Bladegen software. 2.3. Step 3 2.3. Step 3 The grid generation method associated with compressors involves some difficulty in this step. A methodThe grid and generation controls are method required associated to create grids with with compressors a good quality involves for di somefferent difficulty compressor in this designs. step. AEvery method geometric and controls design are of anrequired impeller to requires create grids special with treatment. a good Meshingquality for procedure different is compressor one of the designs.most important Every geometric steps of 3Ddesign analysis. of an impeller requires special treatment. Meshing procedure is one of the Amost reliable important meshing steps is su offfi 3Dciently analysis. fine-grained in the areas with sharp gradients. Determining the dimensionsA reliable of meshing work is very is sufficiently important infine-grained turbomachines in the because areas the with results sharp will gradients. not provide Determining converge theif thedimensions meshes are of too work large, is andvery the important computational in turbomachines time will increase because sharply the if theresults meshes will are not too provide small. convergeTherefore, if the meshes mesh size are selectiontoo large, needs and tothe strike comput a balanceational between time will the increase accuracy sharply of the solutionif the meshes and arethe too computational small. time; this step brings about a trial-and-error process. The meshing of flow domains is aTherefore, tricky procedure mesh size in turbo selection machines needs because to strike of a the balance edges between of blades the and accura cornerscy inof channelthe solution of flow. and the computational time; this step brings about a trial-and-error process. The meshing of flow domains is a tricky procedure in turbo machines because of the edges of blades and corners in channel of flow. Figure 5 shows the meshing of flow domain in TurboGrid. TurboGrid is especially useful for this procedure as it finds inlets and outlets of flow and, gathering information regarding the blades, builds a fine mesh proportional to each place of the domains. The efficiency and the pressure ratio do not change significantly after a certain number of meshing, for as the computational meshes grow smaller, they suggest that the meshing computation is optimal. Sustainability 2019, 11, 5409 7 of 18

Figure5 shows the meshing of flow domain in TurboGrid. TurboGrid is especially useful for this procedure as it finds inlets and outlets of flow and, gathering information regarding the blades, builds a fine mesh proportional to each place of the domains. The efficiency and the pressure ratio do not change significantly after a certain number of meshing, Sustainabilityfor as the computational 2019, 11, x FOR PEER meshes REVIEW grow smaller, they suggest that the meshing computation is optimal.7 of 18

Figure 5. MeshingMeshing of of flow ﬂow domain, domain, TurboGrid TurboGrid software.

The total numbernumber ofof gridgrid nodes nodes is is more more than than 1,250,000 1,250,000 that that created created by theby the structured structured method, method, and andthe nearestthe nearest nodes nodes to the to wallsthe walls are 20are micrometers 20 micrometer far.s So,far. theSo, maximumthe maximum y+ of y+ the of wallsthe walls is around is around 30. 30. 2.4. Step 4 2.4. StepThe 4 compressor can be analyzed by simulating the flow field throughout the whole machine. CFX wasThe thecompressor software usedcan be in thisanalyzed simulation by simulating [26]. Flow the modelling flow field is an throughout important partthe ofwhole 3D simulation. machine. CFXThe CFXwas isthe an software ANSYS used module in this for fluidsimulation simulation, [26]. Flow yet itsmodelling core is designed is an important for turbomachines, part of 3D simulation.therefore it isThe easier CFX tois connectan ANSYS the rotarymodule parts for andfluid stationary simulation, parts yet of its compressors core is designed than other for turbomachines,fluid-modelling therefore modules. it is easier to connect the rotary parts and stationary parts of compressors than Thereother fluid-modelling is a BEP for the modules. base compressor design, and optimization is usually performed at this point;There nevertheless, is a BEP thefor presentthe base research compressor considered design, optimization and optimization in the wholeis usually operating performed range at of this the point;compressor nevertheless, at the nominal the present speed. research [27–29 considered] have shown optimization the code validation in the whol fore turbomachineoperating range flows. of the compressorThe main at the goal nominal of 3D speed. modelling [27–29] is to have observe show detailsn the code of thevalidation flow. Simplifications for turbomachine are flows. rare in this method,The main and goal outcomes of 3D modelling are therefore is to observe realistic details and close of the to actualflow. Simplifications conditions. In are 3D rare modelling, in this method,phenomena and such outcomes as backflow, are therefore vortexes, andrealistic turbulence and close are present to actual that conditions. would be absent In 3D in modelling, 1D and 2D phenomenamodels. One such of the as mainbackflow, criteria vortex in 3Des, modelling and turbulence is thegeometry are present of thethat flow would domain. be absent in 1D and 2D models.An appropriate One of the grid main is thecriteria key toin an3D emodellingffective and is accuratethe geometry modelling of the offlow flow. domain. Grids of domain determineAn appropriate the cost of grid computation is the key and to somean effective basic errors and accurate of modelling. modelling The shape of flow. of gridsGrids is of important domain determineespecially atthe regions cost nearof computation the walls. The and complex some geometrybasic errors of turbo of modelling. machines makes The shape grid generation of grids allis importantthe more important. especially Gridat regions generation near the for walls. rotary Th componentse complex willgeometry be done of byturbo structured machines methods, makes grid and generationthis choice rendersall the more the process important. more Grid efficient generation except for in regionsrotary components such as volute, will where be done a non-symmetric by structured methods,unstructured and gridthis ischoice suitable. renders the process more efficient except in regions such as volute, where a non-symmetricThe following unstructured are important grid aspectsis suitable. which deserve attention in the simulation: TheFor connectionfollowing are of diimportantfferent parts, aspects the Transientwhich deserve Rotor-Stator attention and in Frozen-Rotor the simulation: Simulation method will beFor used. connection This method of different saves detailsparts, the of flowTransien andt works Rotor-Stator not only and on averagedFrozen-Rotor flow Simulation properties. methodThe frozen-rotor will be simulationused. This ismethod applied saves to attain details a steady of flow state and solution works for not various only parts on averaged of the machine. flow properties.To be specific, The the frozen-rotor equipment’s simulati geometryon is does applied not to change attain throughout a steady state the solution interface, for and various the condition parts of theis steady. machine. To be specific, the equipment’s geometry does not change throughout the interface, and the condition is steady. • Flow is steady. • The turbulence method is SST(Menter’s Shear Stress Transport) [30]. This model is designed to obtain the ultimate accuracy in predicting the onset and division of mass flow under adverse pressure gradients. This model has both high performance in observing near-wall flows and secondary flows. The results of computations with this model show significant improvement in flow separation. The high performance of this model has been shown in several validation studies. SST also recommended simulating the boundary layer with high accuracy [31–33]. Sustainability 2019, 11, 5409 8 of 18

Flow is steady. • The turbulence method is SST(Menter’s Shear Stress Transport) [30]. This model is designed to • obtain the ultimate accuracy in predicting the onset and division of mass flow under adverse pressure gradients. This model has both high performance in observing near-wall flows and secondary flows. The results of computations with this model show significant improvement in flow separation. The high performance of this model has been shown in several validation studies. SST also recommended simulating the boundary layer with high accuracy [31–33]. The effects of turbulence were modeled using the standard k-ε turbulence model. To make the • Sustainabilitysimulation 2019 time, 11, x economical,FOR PEER REVIEW wall function is used to resolve the wall flows. It has merits8 of of18 k-ε and k-ω near and far from the walls. • The effects of turbulence were modeled using the standard k-ε turbulence model. To make the simulation time economical, wall function is used to resolve the wall flows. It has merits Boundary conditions at the inlet are temperature and static pressure of air, and at the outlet is of k-ε and k-𝜔 near and far from the walls. mass flow. At the inlet boundary, various forms of boundary condition may be applied. For instance, Boundary conditions at the inlet are temperature and static pressure of air, and at the outlet is mass one may specify the mass flow rate (velocity) or total pressure. For the majority of computational cases, flow. At the inlet boundary, various forms of boundary condition may be applied. For instance, one themay mass specify flow rate the ismass specified flow rate over (velocity) the whole or total inlet pressure. face of the For impeller. the majority An approximateof computational mass cases, flow of 0.287the kg mass/s is flow yielded rate asis thespecified average over inlet the velocity,whole inlet while face theof the measured impeller. state An approximate pressure is appliedmass flow as an averageof 0.287 value kg/s over is yielded the volute’s as the average outlet area. inlet velocity, In order while for the the computations measured state to pressure assess the is applied performance as parameteran average effectively, value over total the pressure volute’s is appliedoutlet area at the. In inlet. order The for impeller the computations is turning withto assess a rotational the speedperformance of 92 k rev parameter/min while effectively, the volute total and pressure diffuser is areapplied both at stationary. the inlet. The impeller is turning with a Followingrotational speed figures of show 92 k rev/min some results while ofthe the volute CFD and simulation. diffuser are Figures both6 stationary. and7 show the 3D numerical simulationFollowing results figures of the centrifugalshow some results compressor of the forCFD the simulation. efficiency Figure and pressure 6 and Figure ratio. 7 show Figure the8 shows 3D thenumerical results of CFDsimulation calculations results forof thethe compressorcentrifugal compressor with streamlines. for the efficiency and pressure ratio. Figure 8 shows the results of CFD calculations for the compressor with streamlines.

0.85

0.8 60 70 0.75

0.7

0.65 Efficiency

0.6

0.55

0.5 2 2.5 3 3.5 4 4.5 5 5.5 Mass Parameter

FigureFigure 6. 6.E Efficiencyﬃciency (%) by 3D 3D simulation. simulation. Sustainability 2019, 11, 5409 9 of 18 SustainabilitySustainability 2019 2019, ,11 11, ,x x FOR FOR PEERPEER REVIEWREVIEW 9 of9 18of 18

1.81.8

1.751.75 60 1.71.7 60 70 1.65 70 1.65 1.6 1.6 1.55 1.55 1.5 1.5 1.45 1.45 Pressure Ratio Pressure 1.4

Pressure Ratio Pressure 1.4 1.35 1.35 1.3 1.3 1.25 1.25 1.2 2 2.5 3 3.5 4 4.5 5 5.5 1.2 2 2.5 3 Mass3.5 Parameter4 4.5 5 5.5 Mass Parameter

Figure 7. Pressure ratio by 3D simulation. Figure 7. Pressure ratio by 3D simulation. Figure 7. Pressure ratio by 3D simulation.

Figure 8. Streamlines in 3D simulation. Figure 8. Streamlines in 3D simulation. Any time one must calculate transient interaction eﬀects at a sliding-frame change interface, a Any time one must calculate transient interaction effects at a sliding-frame change interface, a transient rotor simulation may be utilized. Such simulations are inherently always transient, as they transient rotor simulation may beFigure utilized. 8. Streamlines Such simulations in 3D simulation. are inherently always transient, as they never attain a static condition. This is because the components on each side of a transient sliding Any time one must calculate transient interaction effects at a sliding-frame change interface, a transient rotor simulation may be utilized. Such simulations are inherently always transient, as they Sustainability 2019, 11, 5409 10 of 18 interface are always in relative motion with respect to each other. In a transient, sliding interface, pitch change is handled in the same way as are frozen rotor interfaces: According to the degree of pitch change across the interface, proﬁles in the pitch-wise direction are compressed or stretched. An increasing change of pitch will bring about rapid decreases of accuracy in computation, as is the case with the frozen-rotor condition.

2.5. Step 5 The design loop for impeller forming the final optimization method based on GA analyzes different impeller designs and creates new curves by investigating flow field parameters, including pressure ratio, efficiency, and Y+, as the inputs into the optimization method.

3. Base Compressor The optimized turbocharger compressor consisted of six main blades and six splitter blades with a basic compressor geometry. In simple terms, the turbine and subsequently the compressor spins as long as the air compressor wheel spins and compressed air rotates the turbine. The BEP of this compressor is associated with a speed of 92k rpm and an approximate mass flow of 0.287 kg/s. The nominal pressure ratio of this compressor was approximately 2.2 and its nominal efficiency was 78%. Table1 displays the compressor’s specification.

Table 1. Compressor’s specs.

Value Parameters 2.25 Nominal pressure ratio 0.28 Nominal mass ﬂow (kg/s) 92,000 Nominal rpm 288 Inlet temperature (K) 101 Inlet pressure (KPA) 78% Nominal eﬃciency 0.63 Ratio of relative velocities 22 Inlet diameter at hub (cm) 54 Inlet diameter at shroud (cm) 6 + 6 Number of full and splitter blades 38 Back swept angle (degree) 55 Lean angle (degree) 0.33 Ratio of axial length to diameter

No inlet guide vane (IGV) was present at the inlet of GT4082, although its blades were complex with splitters. The structure was therefore too complicated to be studied and improved.

4. Validating the Results The accuracy and validity of the simulation method was investigated by considering the results of a reliable published article with the most details of the input parameters of the present simulation. The simulation results were compared with those obtained from the cited study. The 3D simulation of the domain was conducted without simplifying the ﬂow. The domain simulated in the optimization process contained the inlet, the impeller, the diﬀuser, and the volute. Figures9 and 10 show this evaluation in which the results of an experimental study associated with the original geometry and a speed of 70 k rpm were used. These results were found to correctly simulate the compressor behavior and to be accurate with a maximum margin of error of 4.2% [14]. SustainabilitySustainability2019 2019,,11 11,, 5409 x FOR PEER REVIEW 1111 of 18 18 Sustainability 2019, 11, x FOR PEER REVIEW 11 of 18

. . FigureFigure 9.9. This is a comparison of efficiency eﬃciency (%) accuracy results inin thethe simulation withwith thosethose associatedassociated Figure 9. This is a comparison of efficiency (%) accuracy results in the simulation with those associated withwith thethe reliablereliable experimentalexperimental study.study.Mass Mass ﬂowflow (kg (kg/s)./s). with the reliable experimental study. Mass flow (kg/s).

. . Figure 10. This is a comparison of pressure ratio accuracy results in the simulation with those associated Figure 10. This is a comparison of pressure ratio accuracy results in the simulation with those with the reliable experimental study. Mass f low (kg/s). associatedFigure 10. withThis theis areliable comparison experimental of pressure study .ratio Mass accu f lowracy (kg/s). results in the simulation with those 5. Resultsassociated and with Discussion the reliable experimental study. Mass f low (kg/s). 5. Results and Discussion 5. ResultsThe results and Discussion obtained from running the optimization method indicate that the splitter blades shouldThe be results shortened obtained and the from slope running of the leading the optimizat edge shouldion method be increased indicate to improve that the the splitter performance. blades FurthershouldThe investigationsbe results shortened obtained designedand from the newsloperunning blades of thethe which optimizatleading start ion atedge the method middleshould indicate ofbe the increased hub, that while the to splitter theirimprove location blades the wasperformance.should ﬁxed be along shortened Further a 30% length investigationsand the of the slope hub designed inof thethe base newleading design. blades edge Thewhich should leading start atbe edge the increased inmiddle the optimal ofto the improve designhub, while hasthe atheirperformance. 40-degree location upward Furtherwas fixed angle, investigations along while ait 30% is quitedesigned length radial of new the with bladeshub a zero in which the angle base start in thedesign. at base the middleThe design. leading of Geometry the edge hub, resultinwhile the ofoptimaltheir the location ﬁrst design optimization was has fixed a 40-degree can along be seena upward30% in length Figure angle, of11 .thewhile hub it isin quitethe base radial design. with Thea zero leading angle edgein the in base the design.optimal Geometry design has result a 40-degree of the first upward optimization angle, while can be it seenis quite in Figure radial 11.with a zero angle in the base design. Geometry result of the first optimization can be seen in Figure 11. Sustainability 2019, 11, 5409 12 of 18 Sustainability 2019,, 11,, xx FORFOR PEERPEER REVIEWREVIEW 12 12 of of 18 18

FigureFigure 11. 11. GeometryGeometry result result of of the the first ﬁrst optimization. optimization.

FigureFigure 1212 showsshows variations variations in in efficiency efficiency versus mass flow flow rate. The The new new impeller impeller is is observed observed to to havehave a a higher higher isentropic isentropic efficiency efficiency at higher mass flows.flows. flows. TheThe The maximummaximum maximum efficiencyefficiency efficiency ofof thethe impellerimpeller waswas alsoalso found found to to be be approximately approximately 2% more than that of the base design.

Figure 12. Comparing the efficiency (%) of the optimized design and base design. Figure 12. Comparing the efficiency (%) of the optimized design and base design.. As may be seen from the performance curve in Figure 12, the new impeller has a higher isentropic As may be seen from the performance curve in FigureFigure 12,12, thethe newnew impellerimpeller hashas aa higherhigher efficiency at higher mass flows. The maximum efficiency of the impeller was also found to be isentropicisentropic efficiencyefficiency atat higherhigher massmass flows.flows. TheThe mamaximum efficiency of the impeller was also found to approximately 2% more than that of the base design, while the pressure ratio [34], of the optimal design be approximately 2% more than that of the base design, while the pressure ratiotio [34],[34], ofof thethe optimaloptimal dropped by about 0.02%, which is negligible compared to the enhancement of efficiency. The pressure design dropped by about 0.02%, which is negligible comparedcompared toto thethe enhancementenhancement ofof efficiency.efficiency. TheThe ratio of the compressor can therefore be assumed to remain constant while efficiency was improved pressure ratio of the compressor can therefore be assumed to remain constant while efficiency was to a relatively favorable value. Figure 13 compares pressure ratios and efficiencies for the new and improvedimproved toto aa relativelyrelatively favorablefavorable value. Figure 13 compares pressure ratiosratios andand efficienciesefficiencies forfor thethe base designs. new and base designs. Sustainability 2019, 11, 5409 13 of 18 SustainabilitySustainability 2019 2019, ,11 11, ,x x FOR FOR PEER PEER REVIEW REVIEW 13 13 of of 18 18

FigureFigure 13. 13. Comparing ComparingComparing efficiency eefficiencyfficiency for for the the optimized optimized design design and and base base design.design. The flow field in the hub and shroud was investigated to find the reason for the increase in TheThe flowflow fieldfield inin thethe hubhub andand shroudshroud waswas investinvestigatedigated toto findfind thethe reasonreason forfor thethe increaseincrease inin efficiency. The Y+ on the walls was not allowed to exceed 30 to maintain the numerical accuracy of the efficiency.efficiency. TheThe Y+Y+ onon thethe wallswalls waswas notnot allowedallowed toto exceedexceed 3030 toto maintainmaintain thethe numericalnumerical accuracyaccuracy ofof boundary layer flow in the simulation of this part. thethe boundaryboundary layerlayer flowflow inin thethe simulationsimulation ofof thisthis part.part. According to Figure 14, a minor shift is observed in the hub in the beginning of the blades, AccordingAccording toto FigureFigure 14,14, aa minorminor shiftshift isis observobserveded inin thethe hubhub inin thethe beginningbeginning ofof thethe blades,blades, followed by changes in the flow field compared to the base design. Although the flow path is smooth followedfollowed by by changes changes in in the the flow flow field field compared compared to to the the base base design. design. Although Although the the flow flow path path is is smooth smooth enough in the compressor inlet, it does not follow the blades but separates from them in the middle due enoughenough inin thethe compressorcompressor inlet,inlet, itit doesdoes notnot followfollow thethe bladesblades butbut separatesseparates fromfrom themthem inin thethe middlemiddle to the hub profile and the Coriolis forces. At this point, splitter blades face a flow with a negative and duedue to to the the hub hub profile profile and and the the Coriolis Coriolis forces. forces. At At this this point, point, splitter splitter blades blades face face a a flow flow with with a a negative negative large incident angle followed by a decrease in efficiency of the compressor, suggesting the major effect andand largelarge incident incident angleangle followed followed byby aa decreasedecrease in in efficiencyefficiency ofof thethe compressor, compressor, suggestingsuggesting thethe majormajor of this part on efficiency. This issue was resolved in the second impeller by shortening the blade in the effecteffect of of this this part part on on efficiency. efficiency. This This issue issue was was resolved resolved in in the the second second impeller impeller by by shortening shortening the the blade blade optimal design and lowering the efficiency drop by preventing the flow from sharply encountering inin thethe optimaloptimal designdesign andand loweringlowering thethe efficiencyefficiency dropdrop byby preventingpreventing thethe flowflow fromfrom sharplysharply the blade. encounteringencountering thethe blade.blade.

. . Figure 14. Comparing streamlines around impeller blades at hub. (left: Optimal; right: Base). FigureFigure 14. 14. Comparing Comparing streamlines streamlines around around impeller impeller blades blades at at hub. hub. (left: (left: Optimal; Optimal; right: right: Base) Base). . The shroud of the impeller can be investigated similarly. Figure 15 shows the streamlines about the shroud.TheThe shroudshroud Turbulence ofof thethe impeller isimpeller much lower cancan bebe in investigatedinvestigated this section andsimilarly.similarly. the blade FigureFigure positions 1515 showsshows do not thethe cause streamlinesstreamlines a major aboutabout drop wherethethe shroud.shroud. new blades TurbulenceTurbulence face a is smootheris muchmuch lowerlower ﬂow. inin thisthis sectionsection andand thethe bladeblade positionspositions dodo notnot causecause aa majormajor dropdrop wherewhere newnew bladesblades faceface aa smoothersmoother flow.flow. Sustainability 2019, 11, 5409 14 of 18 SustainabilitySustainability 2019 2019, ,11 11, ,x x FOR FOR PEER PEER REVIEWREVIEW 14 14 of of 18 18

FigureFigure 15. 15.Comparing Comparing streamlines streamlines aroundaround impellerimpeller at shroud. (left: (left :Optimal; Optimal; right:right Base): Base).. Figure 15. Comparing streamlines around impeller at shroud. (left: Optimal; right: Base).

InIn general, general, the the decreasedecrease inin thethe totaltotal lengthlength of the blades causes causes an an efficiency efficiency improvement improvement by by In general, the decrease in the total length of the blades causes an efficiency improvement by reducingreducing energy energy waste, waste, while while reducing reducing the the area area associated associated with with the the blades blades and and therefore therefore reducing reducing both reducing energy waste, while reducing the area associated with the blades and therefore reducing theboth energy the energy transfer transfer from thefrom blade the blade to the to flow the flow and and the pressurethe pressure ratio. ratio. Simulation Simulation results results suggest suggest the both the energy transfer from the blade to the flow and the pressure ratio. Simulation results suggest simultaneousthe simultaneous presence presence of both of both these these effects, effects, i.e., increasingi.e., increasing efficiency efficiency is accompanied is accompanied by a by minor a minor drop the simultaneous presence of both these effects, i.e., increasing efficiency is accompanied by a minor indrop the pressurein the pressure ratio. ratio. drop in the pressure ratio. InvestigationInvestigation of of the the performance performance of of the the compressor’s compressor’ stalls stall and and choke choke is is also also important. important. Counters Counters for Investigation of the performance of the compressor’s stall and choke is also important. Counters thefor relativethe relative Mach Mach number number are are shown shown to to examine examine the the performance performance ofof the compressor compressor near near the the for the relative Mach number are shown to examine the performance of the compressor near the chokingchoking situation. situation. choking situation. FigureFigure 16 16 shows shows that that thethe maximummaximum Mach numbers emerge emerge near near the the shroud shroud section section where where choke choke Figure 16 shows that the maximum Mach numbers emerge near the shroud section where choke initiates.initiates. In In this this section, section, aa shockshock wavewave startingstarting between two two blades blades restricts restricts the the mass mass flow. flow. initiates. In this section, a shock wave starting between two blades restricts the mass flow.

Figure 16. Mach number near the blades of the optimal impeller. (left: Shroud, center: Midspan and rightFigure: Hub). 16. Mach number near the blades of the optimal impeller. (left: Shroud, center: Midspan and Figureright: Hub).16. Mach number near the blades of the optimal impeller. (left: Shroud, center: Midspan and Furtherright: Hub). studies show that this section, at the throat of the impeller, has a minimum area, and can beFurther identified studies in the show other that conditions. this section, Theat the shock throat wave of the grows impeller, and has entirely a minimum occupies area, the and throat can andbe identified compressorFurther studies in chokesthe showother with thatconditions. an this increase section, The in shockat the the compressor throatwave growsof the mass impeller,and flow.entirely has Given occupiesa minimum that thisthe area, shockthroat and waveand can doesbecompressor identified not emerge chokesin the in theotherwith splitter an conditions. increase area, modifyingin The the shockcompressor the wa leadingve massgrows edgeflow. and does Given entirely not that make occupies this anyshock changesthe wave throat does in and the not emerge in the splitter area, modifying the leading edge does not make any changes in the compressorcompressor choke.chokes with an increase in the compressor mass flow. Given that this shock wave does compressor choke. not emergeThe compressor in the splitter should area, be simulatedmodifying usingthe leading low mass edge flows does tonot investigate make any thechanges stall inin thethe The compressor should be simulated using low mass flows to investigate the stall in the new newcompressor compressor. choke. compressor. FigureThe compressor 17 shows highshould turbulence be simulated and disturbedusing low flowmass fields flows in to the investigate shrouds ofthe both stall designs in the new and Figure 17 shows high turbulence and disturbed flow fields in the shrouds of both designs and inconsistentcompressor. flow paths from the inlet to the outlet. Given the low mass flow and momentum, the fixed inconsistent flow paths from the inlet to the outlet. Given the low mass flow and momentum, the wallsFigure of the 17 volute shows significantly high turbulence affect theand flow. disturbed The flow flow field fields shows in the that shrouds the mass of both flow designs cannot exitand fixed walls of the volute significantly affect the flow. The flow field shows that the mass flow cannot properly,inconsistent which flow causes paths blockage from the and inlet instability. to the outlet. Given the low mass flow and momentum, the exit properly, which causes blockage and instability. fixed walls of the volute significantly affect the flow. The flow field shows that the mass flow cannot exit properly, which causes blockage and instability. SustainabilitySustainability 20192019,, 1111,, x 5409 FOR PEER REVIEW 1515 of of 18 18

Figure 17. Streamlines around blades for optimal (up) and base design (down). (left: Shroud, center : Midspan and right: Hub). Figure 17. Streamlines around blades for optimal (up) and base design (down). (left: Shroud, center: MidspanFewer disturbances and right: Hub). are observed in the mid-span section and a continuous flow appears from the inlet to the outlet of the impeller. Furthermore, a large eddy flow takes a lot of space of the section, Fewer disturbances are observed in the mid-span section and a continuous flow appears from although a correct flow angle is still observed in the impeller inlet and outlet. the inlet to the outlet of the impeller. Furthermore, a large eddy flow takes a lot of space of the section, Major differences can be observed in the stall behavior [35] of the base and optimal designs in the although a correct flow angle is still observed in the impeller inlet and outlet. hub. The most regular flow is observed in the hub section of the base design with separations, whereas Major differences can be observed in the stall behavior [35] of the base and optimal designs in in the optimal blades, the separation is postponed and the splitters present better conditions. the hub. The most regular flow is observed in the hub section of the base design with separations, Tests showed that decreasing mass flow causes the mid-span and the hub quickly to become whereas in the optimal blades, the separation is postponed and the splitters present better conditions. disturbed, which leads to blockage. This information can be used to create a pattern for predicting the Tests showed that decreasing mass flow causes the mid-span and the hub quickly to become stall and surge of compressor. Simulations suggest a 7% postponement in the surge of mass flow in the disturbed, which leads to blockage. This information can be used to create a pattern for predicting optimal compressor. the stall and surge of compressor. Simulations suggest a 7% postponement in the surge of mass flow in6. the Conclusions optimal compressor.

6. ConclusionsThe present article proposed a novel approach for optimizing the impellers of centrifugal compressors by creating and simulating different variations of the base compressor using a hybrid methodThe comprisingpresent article GA and proposed a simulation a novel package approach and defining for optimizing an objective the functionimpellers and of the centrifugal variables. compressorsGA was used by to developcreating aand new simula compressorting different design by variations optimizing of thethe objectivebase compressor function. using GA, as a thehybrid core methodof this method, comprising was usedGA toand optimize a simulation the impeller’s package geometry. and defining GA produces an objective different function generations and the of variables.impellers andGA suggestswas used di tofferent develop designs a new by simulatingcompresso ther design flow using by optimizing a commercial the codeobjective and evaluating function. GA,the performanceas the core of parametersthis method, and was creating used to optimi generationsze the withimpeller’s better geometry. performance. GA produces The optimization different generationsprocess began of impellers by selecting and a suggests turbocharger different compressor designs andby simulating ended with the developing flow using a a new commercial optimal codeimpeller and designevaluating in which the performance the pressure parameters ratio remained and creating constant generations as that of with the basebetter design performance. and the Theefficiency optimization was improved process began by 2%, by while selecting the stabilitya turbocharger of the compressor and improved ended againstwith developing surge by aapproximately new optimal 7%.impeller design in which the pressure ratio remained constant as that of the base designThis and improvement the efficiency in ewasfficiency improved also indicates by 2%, thatwhile extending the stability the study of the and compressor use of CFD simulationimproved againsttools as surge well asby optimizing approximately the performance7%. of turbomachines can consistently be used as a reliable tool forThis moving improvement forward onin theefficiency path toward also indicates sustainable that development. extending the study and use of CFD simulation tools as well as optimizing the performance of turbomachines can consistently be used as a reliable tool for moving forward on the path toward sustainable development. Sustainability 2019, 11, 5409 16 of 18

In the same way, future studies can construct even more conventional models by utilizing reasonable methods of optimization and continuing with more practical lab examinations. As a result of this study, it is predicted that future research will permanently increase the efficiency of the compressor by maintaining the technical specifications of the output fluid to obtain the possibility of replacing fuel-efficient engines with green and economical fuel. Through the effective combination of higher education, advanced research, and industrial practice, these findings from this paper will have a profound impact on theoretical research and commercial development in remanufacturing theory and engineering in the near future.

Author Contributions: M.O. and S.-J.L. conceived of the presented idea and drafted the manuscript. S.M. and H.-T.L. developed the theory, revised, and designed the figures H.-C.Z. and S.-J.L. supervised the findings of this work. All authors discussed the results and contributed to the final manuscript. Acknowledgments: The authors would like to express their gratitude for the financial support provided by the National Natural Science Foundation of China (No. 51975100). This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest.

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