Comprehensive Application of a First Principles Based Methodology for Design of Axial Compressor...

Vishwas Iyengar1

Southwest Research InstituteVR

,

6220 Culebra Road,

San Antonio, TX 78245

e-mail: [email protected]

Lakshmi N. SankarGeorgia Institute of Technology,

270 Ferst Drive,

Atlanta, GA 30332

e-mail: [email protected]

Comprehensive Application ofa First Principles BasedMethodology for Design of AxialCompressor ConfigurationsAxial compressors are widely used in many aerodynamic applications. The design of anaxial compressor configuration presents many challenges. It is necessary to retool thedesign methodologies to take advantage of the improved accuracy and physical fidelity ofthese advanced methods. Here, a first-principles based multiobjective techniquefor designing single stage compressors is described. The study accounts for stage aero-dynamic characteristics and rotor-stator interactions. The proposed methodology pro-vides a way to systematically screen through the plethora of design variables. Thismethod has been applied to a rotor-stator stage similar to NASA Stage 35. By selectingthe most influential design parameters and by optimizing the blade leading edge andtrailing edge mean camber line angles, phenomena such as tip blockages, blade-to-bladeshock structures and other loss mechanisms can be weakened or alleviated. It is foundthat these changes to the configuration can have a beneficial effect on total pressure ratioand stage adiabatic efficiency, thereby improving the performance of the axial compres-sion system. [DOI: 10.1115/1.4006301]

1 Introduction

The compressor is one of the most important componentswithin a gas turbine engine. An inherently complex high-speedflow coupled with highly loaded blades can make the efficientoperation of the compression system a daunting task. In order torun the compressor efficiently, structural instabilities, excessivedeformation of the structure, and flow instabilities such as stalland surge must be avoided or dealt with effectively. The funda-mental operations of a multistage axial compressor were knownand presented to the French Academie des Sciences [1,2] as earlyas 1853. Since then the working of a compressor has been studiedextensively, and compressors have evolved significantly. Thecomplex mechanism associated with the compressors makes itsdesign a challenging task. Traditionally, designers have used acombination of analytical tools, commercially available data, andexpertise in making design decisions. This approach leads to anevolutionary approach for steering the design towards safe realiz-able conditions and configurations. Although increasing the num-ber of stages leads to higher overall pressure rise, it also increasesthe weight and length of the overall compression system.

From an aerodynamic perspective, a more precise 3-D designof the compressor blade is very important as this ensures optimalblade loading. The aerodynamics of a compressor blade is alsoclosely linked to its structural and aeroacoustic responses. Anincreased loading on the compressor blades can cause increasedstructural deformations to the blade, eventually leading to struc-tural failure. An inefficient design of the blades can inherentlylead to increased acoustic response from the blade, from rotor-stator interactions and shock patterns. As discussed by Lakshmi-narayana [3] early designs transonic and supersonic compressorswere failures. Bad compressor designs lead to poor efficiency andlow reliability. Initially, it was believed that the low efficiencies

were due to the shock patterns alone. But after successive designfailures it was recognized that the losses were attributable to flowblockages that are caused by the shocks. Since then significantimprovements have been made in blading design, shock optimiza-tion and hub-to-tip design. A brief summary of the some of theearly designs is given by Hawthorne [4]. Clearly, the design of thecompression system is a multifaceted problem.

In the late 1940s and early 1950s, axial compressor and turbinedesign substantially relied on empirical correlations of data.Howell [5] and Carter et al. [6] performed mean line design ofaxial compressors that relied on cascade data for flow deviation.Cascade data also provided information on profiles and secondarylosses. Modern blade design methods can be classified broadlyinto two approaches, inverse and direct approaches. In inversedesign methods [7–9], desirable flow features on the blade, suchas pressure distribution and/or pressure loading distribution arespecified and the blade geometry is computed in such way that thespecified flow features are produced. If done efficiently, thisdesign method can be applied successfully. In the direct [10–14]approach the blade geometry is analyzed directly by a CFD analy-sis and/or experiments. In this method either the parameters thatdirectly influence the blade section are modified or the (x, y, z)coordinates of the existing blade geometry is altered. The geome-try is subsequently analyzed and the influence of design variableson its overall performance is assessed.

Both the inverse and direct design methods discussed earlierhave their advantages and disadvantages. For example, the directmethod can sometimes be trial-and-error, especially when thedesign parameters are selected in an ad-hoc manner. But it has itsadvantages over the inverse design method, which usuallyrequires a number of inputs, some of which are not always known(e.g., 3-D pressure distribution) so as to produce the desired flowfeatures. Hence, the direct method, which generally does not needsuch detailed knowledge of the flow, is usually preferred.Although the direct design methods used thus far are effective,they do not perform basic blade parameterization, wherein theblade sections are rebuilt based on blade camber line and otherparameters which affect the blade section. In order to consistently

1Corresponding author.Contributed by the International Gas Turbine Institute Division of ASME for pub-

lication in the JOURNAL OF TURBOMACHINERY. Manuscript received July 20, 2011; finalmanuscript received July 21, 2011; published online September 12, 2012. Editor:David Wisler.

Journal of Turbomachinery NOVEMBER 2012, Vol. 134 / 061035-1Copyright VC 2012 by ASME

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rebuild a three-dimensional compressor blade, the blade camberlines, thickness distributions and the blade stack line need to beapproximated as functions of several key parameters. Since theseparameters directly influence the blade section, it is more useful touse these parameters as design variables rather than sweeping orleaning existing blade geometry.

This study aims to develop and demonstrate a systematic inves-tigation to understand the impact of stage design on compressorperformance- total pressure ratio and adiabatic efficiency. A meth-odology will be presented whereby the rotor and stator blades aredesigned based on a parametric description of the blade surfacedesign variables and subsequently optimized using a multiobjec-tive optimization technique. A preliminary application of theproposed methodology was successfully performed by Iyengar[15]. Here a brief overview of the methodology is presented. Aset of state of the art analysis and design tools are next selectedand described along with the multidisciplinary formulation forcompressor design. Then the design methodology is studiedfurther and applied in a more comprehensive manner where amultiobjective optimization is performed, results for which arepresented.

2 Tools and Formulation

Here the tools used for the design methodology are describedbriefly. The study is multifaceted, one that incorporates high fidel-ity computational fluid dynamics and design tools such as designof experiments and response surface methods. A low order cou-pling involving one dimensional flow analysis and design toolshas previously been performed with certain success, but a needfor higher order flow analysis coupled with design tools for opti-mization of compressor stage still exists.

Figure 1 shows a flow chart briefly describing the methodology.In order to study compressor flow details, solution of the 3-D

Navier-Stokes equations is necessary. Previously used analyticalsolutions are only valid to simple flows and configurations andtherefore, numerical techniques are needed for more complexproblems. In an effort to accurately model the flow within a com-pression system in this study, a very robust flow solver SWIFT,developed by Chima [16], is used.

The author refers to Chima [16] for details on the governingequations, boundary conditions and time marching approach usedfor this study. The k-x SST turbulence model is used to model theeffects of turbulent mixing in the compression system. The k-xSST turbulence model is a high fidelity model and it most accu-rately captures the complex flow structure in an axial compressorconfiguration. For the grid generation, a three-dimensional gridcode for turbomachinery-TCGRID developed by Chima [17] atNASA Glenn Research Center is utilized in this study. This codeis capable of generating single block grids as well as multiblockgrids. The single block grids can be of either the H-type orC-type, whereas the multiblock grids must be a C-type gridaround the blade.

This study uses a number of tools to complete the design pro-cess. A method to parametrically design the axial compressorblades is briefly described here; a more detailed discussion isincluded in Ref. [18].

2.1 Parametric Blade Design. In an effort to parametricallymodel the compressor blades in this study, a tool originally devel-oped by Wood [19] called CCGEOM, is used. The tool can beused to facilitate the rapid generation of the flow passage andblading for turbomachinery components. The tool uses a piece-wise smooth cubic spline interpolation method to obtain the ge-ometry. First, the hub and tip geometries are supplied by the useras inputs by specifying the cylindrical co-ordinates (radial andaxial) along each surface. In this study blade camber line anglesand thicknesses at three chord-wise (leading edge, mid-chordand trailing edge) points and three different (hub, mid span andtip) spanwise locations were specified for convenience (Fig. 2).

The present methodology is not restricted to specification of theblade geometry at these three locations. For more complex geo-metries, blade geometry may be specified at more locations.

2.2 Design of Experiments. When designing the blades, anumber of design variables may be involved. The Design ofExperiments technique used to sift through these design variablesis discussed here briefly. The above parametric model gives riseto a number of parameters or “design variables” that may be gen-erated to produce a family of blade surfaces. An independentchange (say two possible changes) to each of these N values willgive rise to 2N combinations, a very large design space. Design ofExperiments (DoE [18]) is a systematic way to plan, conduct andanalyze a series of tests, where the input variables are changedsystematically to extract intelligent information. This method usesa statistical approach that predicts the influences of variablesalong with their interactions on the responses, without the needfor a full factorial analysis. By using DoE, the needed informationcan be extracted with less time and cost. Several methods havebeen developed to carry out the design of experiments, but themain purpose of each method is the same, which is to reduce thenumber of cases required to run while extracting more informationfrom them.

Fig. 1 Flow chart showing the sequence of events in theproposed design methodology

061035-2 / Vol. 134, NOVEMBER 2012 Transactions of the ASME


2.3 Response Surface Methodology. An optimizationmethod is needed to obtain the optimum settings for the designvariables considered. Such a technique, called the response sur-face method, is introduced here. For this work, the use of anall-encompassing model of the physical environment is requiredin order to explore the design space. The exploration of a complexdesign space requires the use of a response surface methodology(RSM). In this study, a commercial software-JMP [20] is used toperform the response surface optimization. Response surfacemethodology acts as a means to find the optimal settings of inputfactors or design variables that maximize, minimize or targetmeasured responses or outcome variables. It utilizes response sur-face equations (RSE’s) that take the form of a polynomial approx-imation of the relationships across given ranges for the inputvariables.

2.4 Output Variables Calculation. In a compression systemthe overall pressure ratio increases. The total pressure ratio is ameasure of the increase in the pressure of the compression system.Total pressure ratio (TPR) of a compression system is defined asthe ratio between the total pressure exiting the compressor to thetotal pressure entering the compressor. If the pressure exiting thecompressor is P02 and the pressure entering the compressor is P01

then the TPR is defined as:

TPR ¼ P02

P01

(1)

The adiabatic efficiency of a compressor is the ratio of the idealinput work needed to raise the total pressure of a working fluidfrom a pressure value P01 to a new value P02, to the actual workneeded on the fluid. The adiabatic efficiency (gad) of the compres-sion system can be found by using:

gad ¼WS

WA(2)

where WS and WA are the isentropic and actual work done on theflow, respectively. These can be found as follows:

WS ¼ m:

cpðT02 sj � T01Þ

WA ¼ m:

cpðT02 � T01Þ(3)

where T01 and T02 are the total temperature are the original totaltemperature and the new total temperatures, respectively. Byapplying isentropic relationship for points 1 and 2 as follows:

T02

T01sj ¼

p02

p01

� �c�1c

(4)

the bar quantities p��; T��

are obtained by the mixed-out averagingtechnique. By substituting Eqs. (3) and (4) into Eq. (2), gives:

gad ¼

p02

p01

� �c�1c

�1

T02

T01

� 1

(5)

In order to gain accurate noise prediction via CFD, it is importantto ensure the boundary conditions used impose nonreflectingboundary conditions. The boundary conditions as used ensure thatnonreflecting properties are imposed at the boundaries. The acous-tic method adopted in this study computes the rotor-wake/statorinteractions through coupled computation. Rotor wake profiles areestablished with three dimensional computations.

A rotor wake influence coefficient (RWIC) is defined to esti-mate the acoustic sound level generated by the rotor-wake/statorinteractions at the rotor/stator exit.

Figures 2 and 3 shows the axial and circumferential locationwhere the RWIC is calculated. Here RWIC is defined as:

RWIC ¼ 10 log10 PAMP=PREFð Þ (6)

where PREF is the reference power equal to 20lPa and PAMP is theroot mean square fluctuating pressure amplitude at the rotor/statorinterface defined as:

P0AMP ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP021 þ P

022 þ P

023 þ � � � þ P02n

n

� �s(7)

where P01;P02::::P

0n are the fluctuating pressures on each blade-to-

blade mesh point at mid span. The fluctuations are extracted fromCFD results based on a circumferentially averaged pressure quantityat mid span. Pressures at each blade-to-blade mesh point at mid spanare subtracted from the circumferentially averaged pressure to givethe fluctuating pressure profile. Upon obtaining the RWIC at eachpoint, the RWIC value will be used in the optimization loop as anobjective function. Benefits of using such method based on steady-state CFD solutions instead of using unsteady-state CFD solutionsfor the pressure levels calculation is that it is computationally less in-tensive, yet the RWIC value provides a way to measure the acousticdisturbance generated by the rotor wake onto the stator.

Fig. 2 Summary of parametric blade design based on design variables- aM,N, bM,N

Journal of Turbomachinery NOVEMBER 2012, Vol. 134 / 061035-3


The sources contributing to compressor noise can originate atdifferent locations in the compression system- on the blade, in thetip gap, rotor-stator interface etc. Typically noise generated due torotor/stator interaction is considered to be important when carry-ing out a compressor stage design. Hence, the use of RWIC atrotor-stator interface as an objective function is justified.

3 Comprehensive Application

Results from the comprehensive application of the design meth-odology are presented here. This method has been applied to arotor-stator stage similar to NASA Stage 35. The newly optimizedconfiguration is termed ‘Optimized Configuration’ for the entiretyof the paper. Results are presented first in form of performancemaps. The visualization of the flowfield is used to interpret theresults. Results from the aeroacoustic analysis are also presentedto substantiate the aerodynamic findings.

3.1 Selection of Design Variables. Eighteen variables wereconsidered for screening; nine for the rotor and nine for the stator-camber line angles at three chord-wise (leading edge, mid-chordand trailing edge) points and three different (hub, mid span andtip) spanwise locations. The objective functions, which in thiscase were total pressure ratio, adiabatic efficiency and rotor wakeinfluence coefficient (RWIC), are obtained from CFD analysisperformed in design of experiments. Pareto curves for total pres-sure ratio, adiabatic efficiency and RWIC are used to narrow thedesign variables based on their contributions. Only common varia-bles that account for approximately 90% contributions to the totalpressure ratio, adiabatic efficiency, and RWIC, are selected.

A closer look at the variables shows, as expected, that theprominent variables are primarily associated with the rotor blade,as compared to the stator blade. This evidently means that, whencompared to the stator, the design of the rotor has a greater impact

on the compressor stage performance functions considered in thisstudy.

In a previous study, equal numbers of rotor and stator designvariables were chosen as design variables. Although it led to apreliminary configuration, the screening performed in this sectionsuggests that a larger set of variables is necessary, especially fromthe rotor design. Ten variables were selected based on its variabil-ity (common variables that account for approximately 90% contri-butions to objective functions), are selected as the decisive designvariables for the design of the compressor stage. The variables aresplit such that 8 variables are for the rotor and the other 2 are forthe stator. The design of experiments is performed again for theten variables. Subsequently a multiobjective optimization wasperformed with the ten selected variables where the total pressureratio, adiabatic efficiency and RWIC were equally weighted. Theoptimizer was executed with the intent of maximizing the stageadiabatic efficiency, stage total pressure ratio and minimizing therotor wake influence coefficient across the rotor-stator interface.

3.2 Optimization Results

3.2.1 Performance Map Comparisons. Performance maps forthe starting configuration and the optimized configuration areshown on Fig. 4 where the total pressure ratio of the stage is plot-ted as function of the ratio of the mass flow rate to the chokingmass flow rate of the respective configurations.

For the optimized configuration, the choking point was found tobe 20.76 kg/sec, compared to 19.8 kg/sec for the starting configura-tion. On comparing the optimized configuration to the starting con-figuration, it can be noticed that the optimized case exhibits onaverage a 2.5% increase in total pressure ratio over the entire oper-ating range. The operating range for the optimized configurationshows a slight improvement over the starting configuration. Figure 5shows the adiabatic efficiency map for the two configurations.From the efficiency map it can be observed that the differencein peak adiabatic efficiency between the two configurations is sig-nificant, especially at peak-efficiency. Near choke conditions, the

Fig. 3 Schematic diagram showing the interface location used for the aeroacousticanalysis

Fig. 4 Performance map comparing the starting configurationto the optimized configuration

Fig. 5 Adiabatic efficiency map comparing the starting config-uration to the optimized configuration



optimized configuration has 2.5% higher peak efficiency than thestarting configuration, which is quite substantial. Some adiabaticefficiency benefits for the optimized configuration are also seen atlower mass flow rates.

3.2.2 Assessment of Blade Loading. In order to make anassessment of the blade performance, the change in blade loadingis considered. Figure 6 (rotor) and Fig. 7 (stator) show the bladeloading comparison between the starting and optimized configura-tions at three spanwise locations (hub, mid span and tip). In thefigures the nondimensional static pressures are plotted againstposition on the blade. Usually the area under such a loading curveis a measure of the amount of loading on the blade surface. It canbe said that the higher the area under the curve, the greater the

loading on the blade. The increased loading corresponds to theblade doing more work on the flow, which can result in higherstage total pressure ratio.

From Fig. 6, it is noticed that the optimized rotor blade experi-ences a slight increase in blade loading at the hub (Fig. 6(a)), midspan (Fig. 6(b)) and tip (Fig. 6(c)) when compared to the startingconfiguration rotor blade, especially at the rotor leading edge. Forthe stator blade it is clear that the optimized configuration has anincreased blade loading at mid span (Fig. 7(b)) and tip (Fig. 7(c))when compared to the starting configuration. The blade incidencehas also been significantly changed going from the starting config-uration to the optimized configuration. The change in incidencecan better align the blade to the flow and also alter the direction ofthe tip vortex. A detailed discussion on direction of tip vortex andits effects on blockages and stage performance will be presentedlater.

3.2.3 Rotor-Stator Aeroacoustic Interaction Comparisons. Inorder to evaluate the rotor-stator interactions, the blade-to-blade

Fig. 6 Rotor blade loading curve comparison at (a) hub, (b)mid span and (c) tip between the starting configuration andoptimized configuration

Fig. 7 Stator blade loading curve comparison at (a) hub,(b) mid span and (c) tip between the starting configuration andoptimized configuration



pressure fluctuations at mid span and mid passage are monitoredin the CFD analysis. The pressure fluctuations caused by the rotordesign provide a way to quantify the potential disturbances andnoise that may propagate downstream.

Figure 8 shows a plot comparing the blade-to-blade pressurefluctuations at rotor exit (stator entrance) for both the starting andoptimized configurations. The fluctuations are measured about acircumferentially averaged pressure value at mid passage. In theplot the y-axis shows the fluctuating pressures (P0) and the x-axisrepresents the blade-to-blade circumferential location where y/y*¼ 0 and y/y*¼ 1 are labeled. It can be observed from the figurethat the pressure fluctuations aft of the rotor blade are less for theoptimized configuration compared to the starting configuration atmost of the circumferential location. Also the magnitude of thepressure fluctuations in the blade wake region is smaller for theoptimized configuration when compared to the starting configura-tion. In the region y/y*¼0.6 to y/y*¼ 1.0, it can be observed thatthe optimized configuration has smaller magnitude and smallerfluctuations when compared to starting configuration.

Figure 9 shows the pressure fluctuations in the radial direction,from the hub to the tip. Here the fluctuations are measured about aradially averaged pressure value. In the plot the y-axis shows thefluctuating pressures (P0) and the x-axis represents the hub-to-tipradial location where z/z*¼ 0 and z/z*¼ 1 are labeled. In theregion z/z*¼ 0.25 to z/z*¼ 0.9, it is observed that the optimizedconfiguration has slightly smaller magnitude and smaller fluctua-tions when compared to starting configuration. In the tip section(z/z*¼ 0.975) the optimized configuration has slightly higher P0

magnitude when compared to the starting configuration.

3.2.4 Flowfield Comparisons. The flow fields for the startingand optimized configurations are compared to quantify the differ-ences observed in the performance maps. Flowfield comparisonsare performed for off-design condition (87% choke massflow)‘OD’ and the design point ‘D’ (97% choke massflow) as shownon performance map in Fig. 6. In Fig. 10, the directions of therotor leading edge tip vortex for the starting configuration and theoptimized configuration are compared. The strengths of the tipvortex are also compared by superimposing the entropy on theparticle path. Two notable differences can be observed. Firstly,the direction and width of the tip vortex for the optimized configu-ration has been significantly altered as it is seen that the tip vortexmoves away from the neighboring blade and is narrower.Secondly, it is observed that the tip vortex entropy strengths areweaker for the optimized configuration when compared to thestarting configuration. The reduced entropy strength along with

Fig. 8 Comparisons of the blade-to-blade pressure fluctuationinfluencing the rotor-wake/stator interactions aft of the rotorblade at mid span

Fig. 9 Comparisons of the hub-to-tip pressure fluctuationsinfluencing the rotor-wake/stator interactions at rotor-statorinterface

Fig. 10 Direction and entropy strength of the rotor leadingedge tip vortex



the altered tip vortex direction results in reduced blockages in themid passage section and will have significant aerodynamic per-formance benefits. The altered tip vortex direction can be corre-lated to the changed rotor blade incidences.

Figure 11 compares the entropy contours at mid passage in themeridional plane for the starting and optimized configurations atthe off-design condition. For the starting configuration a signifi-cant region of high entropy exists in the tip section near the lead-ing edge. This high entropy is attributed to the tip clearancevortex discussed previously. It is noticed that the casing boundarylayer is separated near the rotor leading edge because of the shockand the clearance vortex interactions. In case of the optimizedconfiguration a less pronounced region of high entropy isobserved at the rotor tip, suggesting that the strength of shock-clearance vortex interaction is lesser for the optimized configura-tion. Similar result was also observed in Fig. 10.

Figure 12 compares the entropy contours for an off-design con-dition for the starting configurations and optimized at tip clear-ance section in the blade-to-blade plane. Here the single passageresults have been periodically rotated to reflect adjacent blade pas-sages. On Fig. 12(a), three areas are marked as A- ahead of theblade, B- near the rotor leading edge above the blade and C- midpassage wake region. At point A, the region of high entropy previ-ously present for the starting configuration is now nonexistent forthe optimized case. At the leading edge (Point B) a very rapidchange of entropy is noticed, this is caused by the shock which isrelatively weaker for the optimized case compared to the starting.In the mid passage wake region (Point C), the blade-to-bladewake entropy strength for the optimized configuration is signifi-cantly lower than that for the starting configuration.

Overall, this indicates that the blockages both upstream anddownstream of the rotor blade are reduced. This has a substantial

influence on the performance of the rotor especially at off-designconditions such as the one shown. The improvement in the wakeregion also effects the rotor wake-stator noise interactions andsubstantiates the reduced levels of aero-acoustic interactionsfound earlier for the optimized configuration.

Mach number contours comparing the starting and optimizedconfiguration at 90% span location from the hub for off-design

Fig. 11 Entropy (nondimensional) contour comparisonbetween the (a) starting and (b) optimized configurations, formid passage location at off-design condition

Fig. 12 Entropy (nondimensional) contour comparisonbetween the (a) starting and (b) optimized configurations, fortip clearance section at off-design condition



condition is shown on Fig. 13. On Fig. 13(a) smeared shockemerging from the pressure side (labeled A) at the rotor leadingedge can observed for the starting configuration. This shockpasses through the entire passage eventually ending at the suctionside of the next blade. In the process the shock interacts with theboundary layer on the upper surface of the next blade and can at

times trigger boundary layer separation. From Fig. 13(b) it isnoticed that the shock emanating from the rotor pressure side doesnot exist for the optimized configuration. Instead a weakerdetached shock that loses its strength before it can reach theneighboring rotor blade is observed, and the detached shock doesnot affect the flow on the suction side of the next rotor blade.

Figure 14 shows the effects of the shock and clearance flow onthe casing boundary layer. Blade-to-blade plot of Mach numbercontours for starting (Fig. 14(a)) and optimized configuration(Fig. 14(b)) at the blade tip-off design condition are shown at theright of the figure. This close to the casing the shock is highlysmeared, and the tip vortex can be followed through the shock tothe pressure side of the neighboring blade. Two meridional plotsof Mach number contours above 70% span at two tangential loca-tions (20% and 40%) are shown on the left. The leading edge andtrailing edges are also shown for reference.

In Fig. 14(a), the bottom left plot is near the suction surface ofthe blade shows the clearance vortex just downstream of the leadingedge, followed by a region of low-speed flow. The shock is evidentat near 50% chord, followed by an even larger region of low-speedflow caused by the shock-boundary layer interaction. At 40% tan-gential location the clearance vortex is evident at approximately

Fig. 13 Mach number contour comparison between the (a)starting and (b) optimized configurations at 90% span from hubat off-design condition

Fig. 14 Mach number contour comparison between the (a)starting and (b) optimized configurations at tip off-design con-dition and two meridional planes above 70% span



30% chord. The dotted arrow shows the propagation of the vortexin the azimuthal direction. The solid arrow indicates the chordwisedistance of the clearance vortex from the leading edge.

For the optimized configuration, it is observed from Fig. 14(b) thatthe azimuthal convection of the clearance vortex is slightly different.The tip vortex for the optimized configuration appears to be travelingat higher angle relative to the normal when compared to Fig. 14(b).Also the chordwise position of the same clearance vortex is at agreater chordwise location (�45%), which is again indicated by thelonger solid arrow with leading edge as the reference. By altering thepropagation direction of the tip clearance vortex for the optimizedconfiguration, any blockage effects due to the interaction betweenthe tip vortex and blade-to-blade shocks are reduced.

In the blade-to-blade plane on the right side of Fig. 14(a), astrong shock emerging from the suction side of blade leading edgeis evident for the starting configuration. Comparing this shock toits counterpart in the optimized configuration in Fig. 14(b), it isseen that this shock for the latter is not as strong as the one for thestarting configuration. The shock for the optimized configurationis also not as smeared as compared to the starting configurationand does not extend through the entire passage. It is noticed againthat the interactions between the shock emerging from pressureside and the neighboring blade are very minimal for the optimizedconfiguration compared to the starting one.

Here it is found the aerodynamic changes have a beneficial effecton the performance of the compressor stage. It can be construed thatthe blockage modifications and reduced shock strengths result inincreased total pressure ratios across the stage for no additionalpenalty in the form of decrease in adiabatic efficiency.

4 Conclusions

A first-principles based method to design axial compressorblade configurations has been developed. A systematic study ofthe effects of blade design parameters on compressor performancehas been done. As a part of the work several aspects of bladedesign- aerodynamics and aeroacoustics behavior have been stud-ied. A combination of performance map data and flow visualiza-tion studies have been used to report the findings.

Based on these studies, the following conclusions can be drawn:

• The parametric design of an axial compressor configurationrequires a number of advanced tools. The fidelity level ofthese tools dictates the accuracy and effectiveness of thedesign process. The operation of modern compressor proc-esses is very complex and affected by nonlinear effects suchas shocks, tip vortices, and blockages. High fidelity tools aretherefore necessary. Such high fidelity tools have been exten-sively explored in this study.

• In designing an axial compressor stage a large number ofdesign variables are involved. These include design variablesassociated with the rotor and the stator blades, resulting in alarge set of design of experiments. It was found that the varia-bles associated with the rotor have a bigger influence on theresponse(s) compared to the stator blade variables.

• Axial compressor blades are very sensitive to alterations inblade topology. It was found that by optimizing the bladeleading edge and trailing edge mean camber line angles, phe-nomena such as tip blockages, blade-to-blade shock struc-tures and other loss mechanisms can be weakened oralleviated. These can have a beneficial effect on total pressureratio and stage adiabatic efficiency; therefore improving theperformance of the axial compression system.

• It was found that an aerodynamically optimized blade canalso have aeroacoustic benefits. By optimizing the blade trail-ing edge, the fluctuating aeroacoustic signature from rotor tostator is minimized; therefore resulting in lower rotor wake-stator interactions.

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[14] Keshin, A., Dutta, A. K., and Bestle, D., 2006, “Modern Compressor Aerody-namic Blading Process Using Multi-Objective Optimization,” Proceedings ofGT2006, ASME Turbo Expo 2006, Paper No. GT2006-90206.

[15] Iyengar, V., Sankar, L. N., and Denney R., 2007, “A First-PrincipleBased Methodology for Design of Axial Compressor Configurations,” Proceed-ings of GT2007, ASME Turbo Expo 2007, Montreal, Paper No. GT2007-27513.

[16] Chima, R. V., 2003, “Swift – Multiblock Analysis Code for Turbomachinery,”User’s Manual and Documentation, Version 300, NASA Glenn ResearchCenter.

[17] Chima, R. V., 2003, “TCGRID 3-D Grid Generator for Turbomachinery,”User’s Manual and Documentation, Version 300, NASA Glenn ResearchCenter.

[18] Iyengar., V., 2007, “A First-Principle Based Methodology for Design of AxialCompressor Configurations,” Ph.D. thesis, School Of Aerospace Engineering,Georgia Institute of Technology, Atlanta, Georgia.

[19] Wood, J. R., 1997, CCEOM User Manual, NASA Glenn Research Center.[20] JMP, 2009, Using JMP - User Manual, SAS Institute Inc., Cary, NC.



http://dx.doi.org/10.1115/1.2929092

http://dx.doi.org/10.1115/1.2841776

Comprehensive Application of a First Principles Based Methodology for Design of Axial Compressor...

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