Benini E. - 2005 - Experimetal and Numerical Analyses to Enhance the Performance of a Micro Turbine...

8/2/2019 Benini E. - 2005 - Experimetal and Numerical Analyses to Enhance the Performance of a Micro Turbine Diffuser

1/14

Experimental and numerical analyses to enhance the performanceof a microturbine diffuser

Ernesto Benini *, Andrea Toffolo, Andrea Lazzaretto

Department of Mechanical Engineering, University of Padova, Via Venezia, 1, 35131 Padova, Italy

Received 8 April 2005; accepted 16 September 2005

Abstract

This paper describes design and off-design behavior of a centrifugal compressor of a 100 kW gas turbine used for small scale powergeneration and establishes the guidelines to improve diffuser performance. The first part of the paper deals with the experimental andnumerical tests on the overall machine: An extensive series of tests at different operating points and rotational speeds is performed usingsteady probe measurements at impeller exit and diffuser exit; the numerical model features a mixing plane at impellerdiffuser interfaceand therefore neglects the effect of unsteadiness due to rotorstator interaction. In the second part of the paper, the true time-dependentrotorstator interaction is investigated by means of a numerical model where a sliding mesh technique is adopted instead. The unsteadyresults are then processed and compared with the computed steady flow in the diffuser. Finally, the geometry of the compressor diffuser isoptimized using an evolutionary algorithm coupled with a CFD code. 2005 Elsevier Inc. All rights reserved.

Keywords: Optimization; Evolutionary algorithms; Microturbines; Centrifugal compressors; Diffusers

1. Introduction

Microturbine centrifugal compressors require very com-pact diffusers which must operate at the highest efficiencywhile achieving an adequate pressure recovery and flowturning before the air enters the combustion chamber.Most present design configurations make use of a two-stage vaned diffuser [1]: the first radial row is followed bya 90 annular bend that conveys the flow to an axial deswirlcascade. Little information regarding design guidelines is

provided in the open literature to help accomplish thedesign objectives, and the diffuser apparatus is traditionallydesigned following very basic rules [2].

Two major issues have to be considered for an efficientdesign: the most important of the two deals with the radialcascade, which is in fact the most critical because of thestrong diffusion that occurs and because of the interaction

with the impeller. The other is related to the design of theannular bend and the deswirl cascade: within these compo-nents the flow must not generate excessive losses (especiallythose originating from wall boundary layer growth and sec-ondary flow development) and must leave the blade rowwith low level of swirl (usually not greater than 1525).

In particular, the design of the radial cascade is difficultand involves a lot of designer expertise. The flow leavingthe impeller is fully three-dimensional, featuring highlynon-uniformities between the hub and the shroud and in

the circumferential direction. As a result, a very complexand time-dependent flow field usually occurs in the regionbetween the impeller tip and the diffuser throat due to sec-ondary flows that develop within the machine. This aspecthas been documented by several researchers (see, amongothers [3,4]). Owing to this complexity, some authors haveunderlined the weak points of a simple approach thatattempts to describe the flow entering the diffuser withoutthe direct effect of impeller interaction [57]. On the otherhand, with the help of both experimental and numericalsimulations, other researchers have indicated that the

0894-1777/$ - see front matter 2005 Elsevier Inc. All rights reserved.

doi:10.1016/j.expthermflusci.2005.09.003

* Corresponding author. Tel.: +39 049 8276767; fax: +39 049 8276785.E-mail address: [email protected] (E. Benini).

www.elsevier.com/locate/etfs

Experimental Thermal and Fluid Science 30 (2006) 427440
mailto:[email protected]:[email protected]


2/14

circumferential non-uniformities are less important thanthose occurring from hub to shroud in the neighborhoodof the best efficiency working point [3,8]. Moreover, manyworks report that the fluctuations of the thermo-fluid

quantities as well as of performance parameters decay veryrapidly in the diffuser [912]: the insensitivity of diffuserperformance to the incoming pulsating flow justifies thehighly successful diffuser designs that do not account forrotorstator interaction. This fact has recently encouragedsome researchers to study the flow inside diffusers (withoutthe impeller effect) using computational fluid dynamics(CFD) [13,14], and to develop methodologies to optimizediffuser performance. Regarding the latter, Benini andTourlidakis [15] used a Pareto genetic algorithm andCFD to optimize the shape of a channel diffuser. Zangenehet al. [16] used a 3D inverse design technique to improvethe pressure recovery of a vaned diffuser for a givenimpeller.

This paper deals with performance evaluation and opti-mization of a centrifugal compressor diffuser used in asmall gas turbine (100 kW). The paper is virtually dividedinto three parts. The first refers to the experimental andnumerical investigation on the overall compressor and dif-fuser in both design and off-design conditions. The experi-mental tests are performed according to both ASME andUNI-ISO standards. In the second part, CFD is exploitedto simulate, visualize and analyze the complex flow gener-ated by the rotorstator interaction, with particularemphasis on the unsteady behavior of the vaned diffuser.

The third part deals with the numerical constrained optimi-

zation of the diffuser apparatus (i.e. the radial and deswirlcascades) for maximum aerodynamic efficiency and pres-sure recovery.

The investigated compressor is part of the microturbine

SOLAR T62, which is widely used as an auxiliary powerunit (APU) in military helicopters and as a ground powerunit (GPU) in small light helicopters. The turbine studiedin this work is actually the Titan T62T32, a versionconceived for continuous operation that can also be usedfor ground electric power generation. It consists of a one-stage centrifugal compressor mounted back-to-back witha one-stage radial inflow turbine wheel and an annularreverse-flow combustion chamber (Fig. 1). At the designpoint, the microturbine develops approximately 100 kWshaft power at the rotational speed of 60,000 rpm. Underthese conditions, the pressure ratio is 3.5, the air mass flowrate is 1 kg/s, turbine inlet temperature is 788 C and theexhaust gas temperature is 560 C.

2. Investigation on overall compressor and diffuser

performance

2.1. Experimental apparatus

In order to measure the overall compressor and diffuserperformance, a test rig was set up where the compressorwas driven by the microturbine, as in normal engine oper-ation. A sketch of the test rig is given in Fig. 2. The rig con-sisted of a test-bed where the microturbine was mounted

and connected to an eddy-current brake, which measured

Nomenclature

c chord length, mcn,i ith coefficient of Bezier polygonCp = p3 p2/p02 p2 pressure recovery coefficient of

diffuserF vector of objective functions (f1,f2)g gap, mM Mach number_m mass flow rate, kg/s

n rotational speed, rpmp pressure, PaR radius, mr, rh, z cylindrical coordinates, mt, s time, sT time period, sT temperature, Kx vector of decision variables

x coordinate along chord, mgis total-to-total isentropic efficiencyW generic flow quantityeW 0 unsteady component of the generic flow

quantity

W0

average value of the generic flow quantityh angle between profile leading and trailing edges,

measured in the tangential directionx

= p03 p02/p02 p2 aerodynamic loss coefficient ofdiffuser

Subscripts

0 total1 compressor inlet2 impeller outlet, diffuser inlet3 diffuser outletax axial diffuserclocking circumferential clockinghub huble leading edgeps pressure side

rad radial diffuserss suction sidete trailing edge

428 E. Benini et al. / Experimental Thermal and Fluid Science 30 (2006) 427440


3/14

the torque developed by the engine and the rotationalspeed of the output shaft. Since the compressor intake isnot straight, an inlet pipe (Fig. 3) was built to convey themass flow rate entering the compressor. The mass flow ratewas estimated by measuring the air velocity in the pipe(using a Pitot probe) and air density, as suggested in[17,18]. The mass flow rate was changed by means of a gatevalve positioned at the beginning of the inlet pipe. A set ofcalibrated probes for pressure and temperature measure-ments were placed upstream and downstream of the com-pression stage, as well as in between the impeller anddiffuser. In all, the following measurement probes wereused (see Fig. 2):

1. static pressure probes for p1;2. rack of total pressure probes for p01;

3. total temperature probes for T01;

4. total temperature probes for T02;5. rack of total pressure probes for p02;6. static pressure probes for p2;7. rack of total pressure probes for p03;8. total temperature probes for T03;9. static pressure probes for p3;

10. pitot probe for mass flow rate.

Details on characteristic dimensions and shape of pres-sure and temperature probes at impeller and diffuser exitscan be found in Table 1 and in Figs. 4 and 5. Note that,according to [19], the internal cone angle of total pressureprobes results in a sensitivity angle of about 25 when flowis not aligned with probe axis. This made it possible todetermine compressor performance over the entire operat-ing range. The resolution of pressure and temperature sig-

nals is 100 Pa and 0.05 K, respectively. Calibration of

Fig. 1. Cutaway drawing of the SOLAR T62T32 microturbine.

E. Benini et al. / Experimental Thermal and Fluid Science 30 (2006) 427440 429


4/14

pressure transducers and thermocouples was performed

using instruments having superior metrological characteris-

tics. All the probes showed a highly linear behavior withinthe required range of measurement.

The uncertainty on the mass flow measurement wasdetermined with the help of the standard UNI EN ISO5167 [20]. The uncertainties of the various terms are: uncer-tainty at the 95% confidence level in input power measure-ments is about 0.3%; uncertainty of the electromechanicalefficiency is about 0.9% when input power is 100 kW andelectromechanical efficiency is 75%; uncertainty of the massflow rate is about 0.9%; uncertainty of the pressure ratio

is about 0.6%; uncertainty of the isentropic efficiency is

Fig. 2. Sketch of compressor test rig.

Fig. 3. View of complete compressor test rig.

Table 1Probe characteristics

Impeller exit Diffuser exit

Static pressure No. of holes 4 4Diameter 1 mm 1 mm

Total pressure No. of probes 2 4 racks of 2External diameter 1.2 mm 1.2 mmInternal diameter 0.75 mm 0.75 mmInternal cone angle 30 30

Total temperature No. of probes 2 4External diameter 2 mm 2 mmInternal diameter 1.5 mm 1.5 mmType K KInsulation PTFE PTFE

Fig. 4. Pressure and temperature probes at impeller exit.



5/14

about 1.2%; uncertainty of the compressor total efficiencyis about 0.9%.

All measuring data were collected by a data logger into acomputer that evaluated the performance parameters. As areference for the determination of pressure ratio and isen-tropic efficiency (total-to-total), the ambient pressure andambient temperature were measured in the test room.Ambient humidity was registered as well. Pressure ratio

and isentropic efficiency were evaluated from surge tochoke at different rotational speeds (100%n, 90%n, 80%n,70%n). Surge was determined by identifying the surge phe-

nomena, that is when periodic noise and intense vibrationsoccurred. Diffuser performance parameters were also deter-mined at the rotational speeds defined above.

2.2. CFD simulations

In the numerical study of the compressor, a steady stateanalysis was performed using a mixing plane approachwith a single rotating reference frame. This implies thatonly one impeller channel and one third part of the diffuserwere modeled for simulation, since periodic boundarieswere adopted. Using such an approach, the governingequations are solved in a reference frame that rotates atthe rotational speed of the impeller. The interface betweenimpeller and diffuser was modeled using a mixing plane:thermo- and fluid-dynamic quantities are averaged in thepitchwise direction through the mixing plane, whereas theiractual distribution is maintained in the axial direction. Theoutlet boundary was located at diffuser exit. Structured sin-

gle-block H-type grids were used to mesh both rotating andstationary blade passages (Fig. 6). The overall grid con-sisted of 160,342 nodes which were partitioned in the fol-lowing way: Impeller 28,353 nodes (18%), diffuser131,989 nodes (82%). For simplicity, the impeller was mod-eled without tip clearance. A limited number of grid sensi-tivity studies were carried out to ensure a satisfactoryaccuracy of the flow solver. For this purpose, the compres-sor performance map was calculated with the baseline griddescribed above, as well as with two other grids: the firstwas coarser (approximately 100,000 nodes) and the latterwas finer (approximately 250,000 nodes). Although the

results are not reported here for brevity, the sensitivityanalysis showed that the baseline grid featured a bettercapability, with respect to the coarser one, in capturing

Fig. 5. Pressure and temperature probes at diffuser exit.

Fig. 6. Grid used in CFD calculations.



6/14

the compressor characteristic curve at part load. On theother hand, no noticeable improvement with respect tothe baseline configuration was found using the finer grid.This agrees with the statements reported in [21] and withthe results published in [22]: In particular, in the latterpaper the authors demonstrated that most of the important

effects in centrifugal compressors (i.e. those related to over-all performance) may be captured using a coarse grid ofonly 30,000 nodes, and that nearly all of the results regard-ing efficiency and pressure rise agree well with respect tomeasured values. Therefore, all the results presented herewere obtained using the baseline grid.

Three-dimensional steady-state Reynolds-averagedNavierStokes equations were solved using Fluent5.4 codeby Fluent, Inc. The fluid was supposed to be a compressibleideal gas with constant specific heat capacities. A standardke model [23] was used to account for turbulence in themean flow and a wall function approach was chosen tosolve the boundary layer. All walls (moving and stationary)

were treated as hydraulically smooth and adiabatic. Twosets of boundary conditions, corresponding to the near-choke and near-stall conditions, were considered. Whenoperating conditions close to choking were to be analyzed,the measured values of the total pressure and total temper-ature were applied at impeller inlet; at diffuser exit, themeasured static pressure was instead prescribed: As aresult, the overall mass flow rate of the compressor wasestimated. When the working point approached surge,the values of the mass flow rate and total temperature wereapplied at the inlet, while the measured static pressure wasapplied at diffuser exit. All the calculated quantities were

based on their mass-average values. Using such a steadystate approach it was possible to simulate working condi-tions even beyond the compressor stall point obtainedexperimentally (i.e. at reduced mass flow rates). The lastcomputation for which the CFD code was able to convergewas considered a numerical estimation of the stall pointbecause the unsteady calculations performed beyond thatpoint featured perceivable but unstable separations.

2.3. Experimental and numerical results

The characteristic curves of the overall compressor,obtained both experimentally and numerically, are shownin Fig. 7. The pressure ratio p03/p01 and isentropic effi-ciency gis are plotted as functions of the corrected massflow rate at four values of the rotational speed: n, 0.9n,0.8n and 0.7n. The experimental test showed that the com-pressor has quite a narrow operating range at all rotationalspeeds, and that the normal working point is very close tothe choke line, the corrected mass flow being 1.033 kg/sand the pressure ratio 3.6. In this condition, the isentropicefficiency is about 0.7. This operating point presumablygives adequate margins against the occurrence of compres-sor surge without heavy drawbacks on the efficiency. Atreduced rotational speeds, the pressure ratio curves flatten

out and suggest how careful the operation in these condi-

tions should be in order to avoid the occurrence of flowinstabilities.

In some cases, significant differences were registered in thecode computing accuracy concerning pressure ratio and effi-ciency. At nominal rotational speed, predictions of the pres-sure ratio are excellent over the whole operating range, whilethose regarding the efficiency are less accurate, the maximumdiscrepancy being in the order of 4%. At reduced rotationalspeeds, computed values of the efficiency are quantitativelybetter while those of pressure ratio are worse (i.e. the codeunderestimates the pressure rise). In fact, as the rotational

speed reduces, the computed characteristic curves are shiftedtoward lower values of the mass flow rate, i.e. the code foundsome difficulties in capturing the choke condition. Whileexamining these results, however, the uncertainty on exper-imental data as well as the limitations of the steady stateapproach and of the turbulence model, especially at partload, must be properly taken into account: the use of thesteady-state approach, in particular, is known to give mis-leading results when the operating conditions are very farfrom the nominal one and strong recirculations at impel-lerdiffuser interface are usually observed. In this case, how-ever, the use of a mixing plane still gives acceptable resultsbecause of the narrow operating range of the compressor.Also, the authors believe that some of the discrepanciescould be explained with the absence of the tip clearance inthe numerical simulations, which would limit the maximummass flow rate to some extents and would contribute to areduction in the total pressure ratio and efficiency.

The characteristic curves of the diffuser are reported inFig. 8. They show both the experimental and computed val-ues of the pressure recovery coefficient Cp and the aerody-namic loss coefficient x as functions of the corrected massflow rate. At the nominal speed, the measured pressurerecovery coefficient decreases from 0.5 to 0.45 as the massflow rate increases from stall to choke (i.e. as the angle of

the absolute velocity with respect the tangential direction

Fig. 7. Comparison between experimental and computed compressorcharacteristics.



7/14

increases from 19.4 to 19.9). In such conditions, the aero-dynamic loss coefficient increases from 0.45 to 0.51.

The same tendency is qualitatively observed at reducedspeeds, even though the pressure recovery coefficient ishigher at part load, because the dynamic pressure at impel-ler exit decreases much more than the diffuser pressure

recovery. On the other hand, the aerodynamic loss coeffi-cient reduces slightly at lower mass flow rates due to thefast decrement of the total pressure loss within the diffuser.Because of the lack of measurement probes in the annularbend, it was not possible to isolate the effect of the radialand axial blade rows on overall diffuser performance and,therefore, to establish whether or not the axial deswirlcascade has a negative effect on compressor efficiency andstability. The agreement between the numerical and experi-mental results is good at design nominal speed, whereasareas of relatively poor code accuracy were found atreduced rotational speed. Again, this can be justified ifthe simplifications of the numerical model at impellerdif-fuser interface are taken into account. In any case, theoverall results suggest that the CFD model is sufficientlyaccurate to give realistic indications on diffuser perfor-mance within the overall compressor operating range.

3. Numerical analysis of impellerdiffuser interaction

3.1. Objectives and approach

Viscous and potential effects of rotorstator interactionare comparable in high-speed centrifugal compressors,since the mixing process that rotor blade wakes undergo

is very fast, and the radial gap between rotors and vaned

diffusers is usually very small. As a consequence, a mutualinteraction occurs between the components. The influenceof the impeller on diffuser flow is mainly characterized byviscous effects caused by rotor wakes, while the influenceof the diffuser on the impeller flow is mainly caused bypotential effects [1,24,25]. However, a number of experi-

mental works [3,8,12,26] have shown that the circumferen-tial flow non-uniformity at impeller exit mixes out veryrapidly near the design point, so diffuser flow can be verywell approximated as steady. Dawes [5] and Yamaneet al. [27] compared a steady approach featuring a mixingplane between impeller and vaned diffuser and the corre-sponding fully-coupled unsteady approach. They clearlyshowed the influence of unsteady effects in impeller and dif-fuser, in particular the unsteady effects due to the highlydistorted impeller flow field (both circumferentially andaxially) and those due to the wakes released by impellerblades. In this work, two approaches were investigated:the unsteady-fully-coupled and a steady-decoupledapproach, in which each blade row is treated separatelyby steady computations and flow quantities at the interfaceare averaged in time and in the circumferential direction(while preserving their spanwise distribution). The latterapproach gives satisfactory results provided that a properaveraging is carried out, and this may be not the case whenthe spacing between the blade rows is small. An alternativestrategy is the frozen rotor approach (see, among others[28]), in which steady calculations are performed in a num-ber of fixed impellerdiffuser positions. However it was notexplored here because its features are taken from both theother approaches and do not help to achieve either accu-

racy or computational speediness.

Fig. 8. Comparison between experimental and computed diffuser characteristics.



8/14

The objective of the work is twofold: (i) to achieve a bet-ter understanding of the unsteady flow phenomenainvolved during the interaction; (ii) to assess a quantitativemeasure of flow unsteadiness within the diffuser, in order toverify how much diffuser performance is affected by thepresence of the impeller. The latter objective is fundamen-

tal in the optimization of the diffuser apparatus, describedin the next section, where several time consuming CFD cal-culations are needed to achieve the final solution. A fullyrealistic diffuser can be modeled without the upstreamimpeller provided that the boundary condition at the inter-face accurately simulates the presence of the impeller.

A typical difficulty associated with multi-row simula-tions is that each blade row generally has a different num-ber of blades, and that the ratio between the rotor andstator blades (or its inverse) is not an integer value. Inour case, due to the lack of periodicity in the blade numberof compressor components, the number of blades of thediffuser was modified (12-blades radial and 36-blades des-

wirl), in order to simplify the flow domain and reduce thecomputational effort. As a result, it should not be expectedthat the computed solution represents accurately the realflow within the original configuration. However, the pur-pose here was much more focused on assessing a method-ology for studying the interaction rather than simulatingthe real flow. The resulting flow domain was divided intothree blocks, each representing a quarter of the real physi-cal domain, for the impeller, the radial and deswirl diffus-ers, respectively. The assembled grid consisted of about100,000 nodes. The impeller was modeled without tipclearance.

The unsteady statorrotor simulations were carried outusing the CFD code FluentTM, by Fluent Inc., where a slid-ing mesh technique was utilized. The unsteady 3D Rey-nolds-averaged NavierStokes (RANS) equations for acompressible ideal gas were solved along with a SpalartAllmaras turbulence model [29]. Standard wall functionswere used to link the solution variables at the near-wallcells and the corresponding quantities on the wall. Bound-ary conditions were imposed as follows: the total pressureand total temperature were applied at impeller inlet(p01 = 101325 Pa, T01 = 288.1 K), where the flow was sup-posed to be swirl-free; a constant value of the static pres-sure was maintained at the outlet of the deswirl diffuser(p3 = 193913 Pa).

3.2. Results

The unsteady computations were carried out using atime step Dt = 4 106 s, which corresponds to 1.47 ofimpeller rotation. The chosen time step was the maximumthat made it possible to capture the flow unsteadiness withreasonable accuracy avoiding the increase of the computa-tional effort beyond unacceptable limits. An unsteady runrequired about 50 h to reach a periodic solution on aWorkstation AlphaServer ES40, clock 667 MHz, 1.5 GB

RAM. The periodicity of the pressure signal at a point

located between impeller and diffuser blades was consid-ered as a convergence criterion, which was typically satis-fied after one to two complete impeller revolutions.

The time average of the unsteady solution was calcu-lated by means of an in-house post-processing tool in orderto isolate the unsteady components of the flow quantities.

The unsteady component of the generic quantity W(r,h, z, t) was calculated as follows:

eW0r; h;z; t Wr; h;z; t Wr; h;zWr; h;z

1

where

Wr; h;z 1

T

ZT0

Wr; h;z; tdt 2

The instantaneous contours of pressure and Mach num-ber and of their unsteady components ~p0 and

eM

0are

reported in Figs. 9 and 10, respectively, on a plane which

cuts blade passages at impeller exit midspan. These plotscorrespond to various instants in time during the periodT, i.e. the time required for the rotor blade to cover the dis-tance corresponding to one rotor pitch. Note that quanti-ties are time-averaged with reference to the absoluteframe in the diffuser, whereas, quantities are time-averagedwith reference to the rotating frame in the sliding mesh por-tion including the impeller. As a consequence, a discontinu-ity at the impellerdiffuser interface appears in Figs. 9(b)and 10(b).

The jet flow leaving the impeller is periodically cut bythe diffuser leading edge, and this causes periodic pressure

fluctuations on both impeller trailing edges and diffuserleading edges. Thus, the largest part of flow unsteadinesscomes from the potential effect, which follows the periodiccycles of rotating blade positions relative to the stationaryone, and is confined in the semi-vaneless gap between theimpeller and radial diffuser. The magnitude of suchunsteadiness is in the order of 10% for both the pressureand Mach number, the core being located very close to themiddle of the gap between the rotating and stationary com-ponents. As the flow mixes out in the diffuser, the unstead-iness reduces rapidly and the flow becomes nearly steady. Itis worth noting that the flow within the radial diffuser, inparticular toward the trailing edge, is almost insensitiveto the unsteadiness generated by the impeller. However,quite large fluctuations of the Mach number can be identi-fied in the diffuser along the surfaces of the radial cascade,both on the pressure and suction sides. These fluctuationsare probably due to the fact that the stagger angle of theradial cascade is not properly matched with the angle ofthe flow leaving the impeller. Therefore, the flow acceler-ates or decelerates according to the reciprocal positionbetween the impeller and diffuser blades, i.e. according toboth the interception of the jets from the impeller by theradial profile itself (wake effect) and the oscillations ofthe pressure field in the gap between impeller and diffuser

cascades (potential effect).



9/14

The unsteady performance coefficients (x and Cp) of theoverall diffuser apparatus were calculated as well, and theirvalues are reported in Fig. 11 as a function of the impellerrevolutions counter. The mass-flow weighted average val-

ues were calculated and made dimensionless with respect

to their time average value: it can be noted that the fluctu-ations ofx are less than 0.5% and those of Cp are evenless. The time averaged values ofx and Cp were then com-pared with those obtained from a steady simulation regard-

ing the diffuser alone, i.e. without the impeller. This

Fig. 9. Instantaneous contours of pressure at diffuser midspan for different impeller blade positions (a) and instantaneous contours of unsteady pressure(b).

Fig. 10. Instantaneous contours of Mach number at diffuser midspan for different impeller blade positions (a) and instantaneous contours of unsteadyMach number (b).



10/14

simulation was carried out using the same solver, settingsand grid: the values of the relevant quantities of theunsteady solution, averaged with respect to time and massflow rate, were assigned as boundary condition at diffuserinlet. In this way the dynamic effect of the impeller wasneglected. In particular, time- and circumferentially-mass-averaged values of the total pressure and total temperaturewere applied at diffuser inlet; time- and mass-averagedvalue for the static pressure was instead fixed at diffuseroutlet.

The results of the steady calculation are given in Fig. 11

and compared with those of the unsteady computation.The differences are virtually negligible: 1.9% in x, 0.6%in Cp. These results apparently demonstrate that, fromthe point of view of diffuser performance, the presence ofthe impeller can be reproduced by assigning averaged andsteady boundary conditions at impeller outlet.

4. Optimization of diffuser performance

4.1. Objectives and approach

In this section, a numerical multi-objective optimization

of the radial and deswirl cascades of the centrifugal com-pressor is accomplished through an iterative procedurebased on the combination between a Multi-Objective Evo-lutionary Algorithm (MOEA) and a CFD model of the dif-fuser. The aim is to develop a set of diffuser designsachieving maximum pressure rise (maximum Cp) and min-imum total pressure loss (maximum 1 x) at the designcondition (see previous section). These designs have alsoto fit into the radial and axial sizes of the original one, per-haps adjusting the radius between the radial and the des-wirl sections. The optimization problem is to maximizethe two-objective function:

Fx f1;

f2 Cp;

1 x 3

where x is the vector of design optimization parameters,that is the decision variables of the problem.

The chosen objectives cannot be satisfied simultaneouslyby a single design, since maximum pressure rise is achievedthrough high aerodynamic loading on blade profiles,resulting in higher total pressure losses, whereas minimum

total pressure loss is obtained using low solidity cascades tominimize friction losses, without altering too much flowtangential direction. Thus, Pareto optimality is used torank the solutions examined during the optimization pro-cess and to obtain the true trade-off solutions betweenthe two objectives (Pareto front). A special evaluationmethod is applied in order to improve the search capabili-ties of the MOEA and to spread the optimal solutions asuniformly as possible along the Pareto front [30].

4.2. Definition of design parameters

Since the optimal designs have to fit into the overall size

of the original one in the meridional plane, the followingdimensions are chosen as optimization parameters (seeFig. 12): the radius Rhub of the arc linking the radial andthe deswirl sections of the diffuser in a meridional plane;the radial coordinate Rle,rad of the radial profile leadingedge; the radial clearance gte,rad between the radial profiletrailing edge and the radius linking the two sections; theangle hrad between the radial profile leading and trailingedges, with respect to the tangential direction; the axialclearance gle,ax between the deswirl profile leading edgeand the radius linking the two sections; the angle haxbetween the deswirl profile leading and trailing edges, with

respect to the tangential direction; the tangential clockinghclocking between the leading edges of the radial and thedeswirl profiles.

The number of blades of both radial and deswirl sec-tions (12 and 36, respectively) is the one used in the previ-ous section. The shape of blade profiles is described usingtwo Bezier parametric curves (one for the pressure sideand one for the suction side). The non-dimensional Carte-sian coordinates of each curve x, yps and x, yss are definedby n + 1 control points constituting the Bezier polygonaccording to the following expression:

fxt;yps

t;yss

tg Xn

i0

cn;iti1 tnifxi;y

ps;

i

;yss

;

i

g 4

where t 2 [0, 1] is the non-dimensional parameter andcn,i = n!/(i!(n i)!). The n + 1 control points coordinatesxi, yps,i, yss,i are defined as follows:

xi 0; 0;x2; . . . ;xn2; 1; 1

yps;i 0; dle; . . . ;ycl;i di; . . . ; dte; 0

yss;i 0; dle; . . . ;ycl;i di; . . . ; dte; 0

5

where dle and dte fix the thickness of the leading and trailingedges, respectively, and ycl,i and di are the actual optimiza-tion parameters for blade shape geometry. This parameter-

ization is inspired by the well-known practice of

Fig. 11. Comparison between steady and unsteady performance coeffi-cients of the diffuser apparatus.



11/14

superimposing a thickness distribution to a chamber lineand avoids the generation of intersecting pressure andsuction side curves. The geometry of the diffuser radialand deswirl blades is described here using seven and sixcontrol points, respectively (6 and 4 decision variables).The total number of optimization parameters is therefore17.

According to the geometrical constraints, the ranges ofvariation chosen for most optimization variables are nar-row and centered around the corresponding values of theoriginal design. The main exception to this criterion is rep-resented by the value ofhrad, which is varied in a range thatdoes not include the original value. The shape of the des-wirl profile is also allowed to vary more freely than thatof the radial profile. The ranges of variation for all the opti-

mization variables are summarized in Table 2.

4.3. Results and discussion

The optimization algorithm was run for 40 generationswith a population size of 50 individuals. The most impor-tant design parameters and the corresponding objectivefunction values for the last generation of solution are pre-sented in Fig. 13. Note that performance indexes of the ori-ginal design are too low (Cp = 0.45 and 1 x = 0.5) toappear in the Figure. It is apparent that all the individualsfall in a narrow strip of the plane defined by the two objec-tive functions Cp and 1 x. As a matter of fact, the con-flict between the objectives seems of little account, but

this is simply because of the tight ranges of variationassigned to the optimization variables. The Pareto frontis made of only two individuals, one of them maximizingpressure recovery (marked in red) and the other minimizingtotal pressure losses (marked in blue). These optimal solu-tions are compared to the original design in Fig. 13.

4.3.1. The radial profile

The shape of the optimal radial profiles is very similar tothe original one because of the limits imposed on the vari-ation of its Bezier control points. On the other hand, thestagger angle, which is varied in a wider range, seems tobe the most significant design parameter. The optimizedsolutions have a much lower value ofhrad than the originaldesign (40). This results in higher pressure recovery,because of reduced tangential velocity components, as wellas in lower total pressure losses because of better incidenceangles and less friction on shorter profiles. hrad beingapproximately the same, the actual conflict between thetwo objectives owing to two opposite trends toward shorterprofiles to minimize losses and toward longer profiles tomaximize pressure rise.

The radial coordinate of the leading edge Rle,rad tendstoward its maximum value to shorten the profile and toallow an initial pressure recovery without blade friction,

that is with lower total pressure losses. This fact agrees with

Fig. 12. Definition of optimization parameters.

Table 2Ranges of optimization parameters

Variable Unit Original Min Max

Rhub mm 9.5 8 12Rle,rad mm 84 82 86

gte,rad mm 3.5 2 6hrad 40 25 35

y1,rad 0.02 0.015 0.025y2,rad 0.055 0.05 0.06y3,rad 0.06 0.04 0.08d1,rad 0.03 0.025 0.035d2,rad 0.065 0.055 0.075d3,rad 0.055 0.035 0.075gle,ax mm 2.5 1 3hax 5 2 8

y1,ax 0.12 0 0.2y2,ax 0.12 0 0.2d1,ax 0.055 0.02 0.1d2,ax 0.055 0.02 0.1hclocking 6.1 0 10



12/14

the experimental results published in the literature abouthigh-speed compressors (see, among others [31]). In fact,as the absolute Mach number of the flow leaving the impel-ler is quite high, a longer vaneless gap is needed to reducethe Mach number level, and therefore losses, before enter-ing the vanes. The optimized profiles are also less thick

than the original ones, resulting in a higher pressure rise.Even though flow separation near the trailing edge is morelikely for thinner profiles, it does not happen in this casedue to the small ranges of variation imposed on the shapeof the profile.

4.3.2. The meridional channel

The radius Rhub linking the radial and the axial sectionof the meridional channel tends to its maximum value forboth the optimal designs. This is reasonable, since the lossrelated to secondary flows in the bend and downstream ofit is reduced. The enlargement of the gap between the radialcoordinate of the trailing edge and the beginning of thecurvature may also be responsible for this reduction.

4.3.3. The deswirl profile

The orientation of the deswirl profile in the optimizeddesigns cannot be analyzed separately from the flow devia-tion imposed by the radial cascade of the diffuser. Sincehrad is lower than in the original design, the tangentialvelocity of the flow entering the deswirl cascade is lowerbecause of the conservation of the tangential momentum.On the other hand, the meridional velocity is also lowerbecause of the conservation of meridional momentum,since Rhub is larger in the optimized designs. The latter

effect prevails over the former, and the result is a stagger

angle, measured by hax, that is higher than in the originaldesign. Even though the vanishing of the tangential compo-nent through the deswirl cascade would result in the max-imum pressure recovery, the exit angle of the optimizeddesigns is far from the value that would fulfill this condi-tion. Perhaps the chord of the profile is too short to accom-

plish the ideal deviation at the expense of a negligibleincrease in total pressure losses. Finally, the optimizedclocking hclocking is achieved when the wake of the radialprofile wraps one of the deswirl profiles.

5. Practical significance/usefulness

The methodology described in the first part of the papersignificantly reduces the computational effort required toperform CFD analyses on rotating machinery featuringhigh-speed flows, compressibility issues, rotor/stator inter-action and problems related to the definition of properboundary conditions. This can be achieved without compro-mises on the accuracy of the numerical results, as certified bythe validation presented. The ultimate goal is to use suchapproaches to tackle complex optimization problems usingadvanced mathematical techniques. From this point of view,evolutionary algorithms show very attractive potentials inthe exploration of wide search spaces with many decisionvariables and complex and conflicting objective functions.

6. Conclusions

In this paper, experimental and numerical analyses wereused to achieve performance enhancements of a micro-

turbine diffuser.

Fig. 13. Results of optimization.



13/14

First of all, a methodology for testing the centrifugalcompressor was presented. A test rig was set up andequipped with pressure and temperature probes at impellerinlet and outlet and at diffuser exit. The tests were carriedout according to both ASME and UNI-ISO standards. Anumerical model based on 3D CFD was also carried out

and validated against the experimental data. The numericalresults regarding the pressure ratio at the nominal speedagree with the experimental data; those concerning theisentropic efficiency show poorer agreement (computed effi-ciency is higher). At reduced speeds, the numerical modeloverestimates the pressure ratio to some extent, whereascalculated efficiency is much closer to the measured one;at the same time, the mass flow rate at choking is a littlelower than the one observed experimentally. These factsmay be explained by the absence of the tip clearance inthe numerical model of the impeller (see also the discussionin Section 2.3). The diffuser maps showed that the pressurerecovery and aerodynamic losses are apparent functions of

the mass flow rate for a given compressor rotational speed.The absence of measurement probes in the space betweenthe radial and deswirl blade rows did not make it possibleto describe the behavior of each cascade, even though it isknown that the actual pressure recovery in the last row isnot likely to be high; its function is mainly to remove swirlbefore the flow enters the combustor. However, the effectof the axial deswirl diffuser should be investigated furtherin order to establish its influence on compressor efficiencyand stability. The numerical results showed that the steadyapproach is sufficiently accurate to predict the characteris-tics of the diffuser, at least for the nominal rotational speed.

At reduced speeds, in particular at part loads and nearcompressor stall, somewhat poor agreement with theexperimental data suggests that diffuser performance couldbe significantly influenced by the jet-wake and recirculationflow structures which the CFD model, being based on amixing plane approach, obviously was not able to capture.

In the second part of the paper, two approaches for theanalysis of impellerdiffuser interaction in the centrifugalcompressor stage were examined. The first approach wasbased on the fully-coupled unsteady solution of the flowfield; the latter assumed time- and space-averaged bound-ary conditions at the interface between the impeller and dif-fuser with which a steady and decoupled solution wasobtained. The unsteady simulation made it possible to ana-lyze and understand the details of the main sources of flowfield fluctuations. The amplitudes of these fluctuations areremarkable only in the semi-vaneless gap, whereas the dif-fuser blade channel is not substantially involved in thesephenomena. This fact is confirmed by the agreement withthe results of the steady simulation, performance indexesbeing virtually identical. The results of both approacheshighlight that some of the geometrical characteristics ofthe diffuser are not properly matched to the flow leavingthe impeller, leading to a poor overall diffuser performance.

In the third part of the paper, the diffuser design was

optimized focusing the attention on the cascade parame-

ters, and leaving the size of the meridional channelunchanged. The aim was to obtain the maximum pressurerise at the minimum total pressure loss. The conflictbetween the two objective is minimal, owing to the tightconstraints imposed to the chosen design variables. Themost significant differences from the original design are

the lower stagger angle of the radial profile, leading tohigher pressure rises, and the lower chamber of the deswirlprofile, which actually hardly deflects the flow resulting inlower total pressure losses. The optimization of diffuserperformance focusing on the design point only is meaning-ful, since the operating range of this microturbine centrifu-gal compressor is very narrow. In off-design conditions, infact, choking or stall occur before performance drops dueto unsatisfactory design solutions.

References

[1] C. Rodgers. Microturbine cycle options, ASME Paper 2001-GT-0552,

2001.[2] D. Japikse, Centrifugal Compressor Design and Performance,

Concepts ETI Inc., Wilder, Vermont, 1996.[3] M. Inoue, N.A. Cumpsty, Experimental study of centrifugal com-

pressor discharge flow in vaneless and vaned diffusers, ASME Journalof Engineering for Gas Turbines and Power 106 (3) (1984) 455467.

[4] D. Bonaiuti, A. Arnone, C. Hah, H. Hayami. Development ofsecondary flow field in a low solidity diffuser in a transonic centrifugalcompressor stage, ASME Paper GT-2002-30371, 2002.

[5] W. N. Dawes. A simulation of the unsteady interaction of acentrifugal impeller with its vaned diffuser: flow analysis, ASMEPaper 94-GT-105, 1994.

[6] K. Sato, L. He. A numerical study on performance of centrifugalcompressor stages with different radial gaps, ASME Paper 2000-GT-462, 2000.

[7] Y.K.P. Shum, C.S. Tan, N.A. Cumpsty. Impellerdiffuser interactionin centrifugal compressor, ASME Paper 2000-GT-0428, 2000.

[8] Y. Senoo. Vaneless diffusers and vaned diffusers. Flow in CentrifugalCompressors, VKI Lecture Series 1984-07, 1984.

[9] M.V. Casey, M. Eisele, Z. Zhang, J. Gulich, A. Schachenmann. Flowanalysis in a pump diffuser, Part 1: LDA and PTV measurements ofthe unsteady flow, ASME Paper, FED Summer Meeting, Symposiumon Laser Anemometry, 1995.

[10] M.V. Casey, M. Eisele, F.A. Muggli, J. Gulich, A. Schachenmann.Flow analysis in a pump diffuser, Part 2: validation of a CFD code forsteady flow, ASME Paper, FED Summer Meeting, Symposium onLaser Anemometry, 1995.

[11] F.A. Muggli, D. Wiss, K. Eisele, Z. Zhang, M.A. Casey, P. Galpin.Unsteady flow in the vaned diffuser of a medium specific speed pump,ASME Paper 96-GT-157, 1996.

[12] S. Deniz, E.M. Greitzer, N.A. Cumpsty, Effects of inlet flow fieldconditions on the performance of centrifugal compressor diffusers:Part 2Straight-channel diffuser, ASME Journal of Turbomachinery122 (1) (2000) 1121.

[13] P. Dalbert, G. Gyarmathy, A. Sebestyen. Flow phenomena in vaneddiffuser of a centrifugal compressor, ASME Paper 93-GT-53, 1993.

[14] E. Casartelli, A.P. Saxer, G. Gyarmathy. Performance analysis in asubsonic radial diffuser, ASME Paper 98-GT-153, 1998.

[15] E. Benini, A. Tourlidakis. Design optimization of vaned diffusers forcentrifugal compressors using genetic algorithms. AIAA Paper 2001-2583, 2001.

[16] M. Zangeneh, D. Vogt, C. Roduner. Improving a vaned diffuser for agiven centrifugal impeller by 3D inverse design, ASME Paper GT-2002-30621, 2002.

[17] ASME PTC 10-1997. Performance test code on compressor and

exhausters, ASME Code, 1997.



14/14

[18] UNI 10727. Fluids flowrate in closed circular conduitsvelocitymeasurement method on one point of section, Italian Standard, 1998.

[19] D. Japikse. Advanced experimental techniques in turbomachinery,Principal Lecture Series No. 1, Concepts ETI, Inc. Norwich, 2000.

[20] UNI EN ISO 5167, Measurement of fluid flow by means of pressuredifferential devices, European Standard, 1997.

[21] J.D. Denton. Turbomachinery Design Using CFD, AGARD LectureSeries 195, 1994.

[22] H. Tsuei, K. Oliphant, D. Japikse, in: The Validation of Rapid CFDModeling for Turbomachinery, IMechE Conference, London, 1999.

[23] B.E. Launder, D.B. Spalding, The numerical computation of tur-bulent flow, Computational Mathematics in Applied MechanicalEngineering 3 (1974) 269289.

[24] C. Pfleiderer, Die Kreiselpumpen fur Flussigkeiten und Gase,Springer-Verlag, Berlin, Gottingen, Heidelberg, 1961.

[25] R.C. Dean. On the unresolved fluid dynamics of the centrifugalcompressor, Advanced Centrifugal Compressor, ASME Gas TurbineDivision, 1971.

[26] V.G. Filipenco, S. Deniz, J.M. Johnston, E.M. Greitzer, N.A.Cumpsty, Effects of inlet flow field conditions on the performanceof centrifugal compressor diffusers: Part 1Discrete-passage diffuser,ASME Journal of Turbomachinery 122 (1) (2000) 110.

[27] T. Yamane, H. Fujita, T. Nagashima. Transonic discharge flowsaround diffuser vanes from a centrifugal impeller, ISABE Paper 93-7053, 1993.

[28] Z. Liu and D.L. Hill. Issues surrounding multiple frames of referencemodels for turbo compressor applications, in: Proceedings, 15thInternational Compressor Engineering Conference at Purdue Uni-versity, West Lafayette, 2000.

[29] P.R. Spalart, S.R. Allmaras. A one-equation model for aerodynamicflows, AIAA Paper 92-0439, 1992.

[30] A. Toffolo, E. Benini, Genetic diversity as an objective in multi-objective evolutionary algorithms, Evolutionary Computation 11 (2)(2003).

[31] R.H. Aungier, Centrifugal Compressors a Strategy for AerodynamicDesign and Analysis, ASME Press, New York, 2000, p. 2.


Benini E. - 2005 - Experimetal and Numerical Analyses to Enhance the Performance of a Micro Turbine...

Documents

Transcript of Benini E. - 2005 - Experimetal and Numerical Analyses to Enhance the Performance of a Micro Turbine...