Francesco MelinoIMEM, CNR,

Parma, Italy

Mirko MoriniMechLav, Universita di Ferrara,

Ferrara, Italy

Antonio PerettoDIEM, Universita di Bologna,

Bologna, Italy

Michele Pinelli

Pier Ruggero Spina

Dipartimento di Ingegneria,

Universita di Ferrara,

Ferrara, Italy

Compressor Fouling Modeling:Relationship BetweenComputational Roughness andGas Turbine Operation TimeGas turbine axial compressor performance is heavily influenced by blade fouling. As aresult, the gas turbines efficiency and producible power output decrease. Performancedegradation of an axial compressor stage due to fouling can be analyzed by means ofsimulation through computational fluid dynamics (CFD) codes. Usually these methodsreproduce the deteriorated blades by increasing their surface roughness and thickness.Another approach is the scaling of compressor stage performance maps. A model basedon stage-by-stage techniques was presented in a previous work. This model is able to esti-mate the modifications of the overall compressor performance map as a function of theoperating hours. The aim of the present study is to combine these two differentapproaches in order to relate the increase of blade computational surface roughness withcompressor operating hours. [DOI: 10.1115/1.4004739]

Introduction

Environmental conditions of the site in which a gas turbine or acombined cycle power plant are installed strongly influence theirperformance. In particular, compressor fouling, which is one ofthe main reasons for gas turbine compressor performance degra-dation, is heavily influenced by the quality of the air swallowedby the compressor. It is estimated that, typically, compressor foul-ing accounts for 70% to 85% of the total gas turbine performanceloss during continuous operation [1].

The effect of compressor fouling is the reduction of the inlet airmass flow rate, isentropic efficiency, and pressure ratio. Theseinfluence the coupling between the compressor and turbine andresult in a loss of the gas turbine power output and overall effi-ciency. The loss of the gas turbine power output can range from 2%under favorable conditions, to 15%–20% under adverse conditions[2].

Axial compressor fouling is caused by the adherence of smallparticles to blades surfaces; this causes an increase of blade rough-ness and, as a consequence, a change in the shape of the airfoil.

In spite of the presence of the filters in the inlet duct, the par-ticles can reach the axial compressor due to their small diameter,which is generally smaller than 2–10 lm [3]; usually these par-ticles can be removed by adequate compressor washing.

In recent years, many authors have studied this matter, describ-ing the gas turbine performance degradation mechanisms [1–6],developing analytical models [7–9], and focusing on diagnosticsand maintenance aspects [10,11].

The aim of this study is to combine two different approaches inorder to estimate the performance degradation of a compressorstage due to fouling, and to understand the relationship betweencompressor operating hours and the increase in blade computa-tional surface roughness. The first approach provides the perform-ance changes due to fouling of an actual compressor stage throughCFD simulations [12,13]. The second approach makes it possibleto estimate the overall compressor performance map modifica-tions due to fouling as a function of operating hours. Thisapproach uses a compressor stage-by-stage model and a scalingtechnique of the compressor stage performance maps and is

included in the IN.FO.G.T.E. code [14], which was tuned accord-ing to results available in literature [15].

Axial Compressor Fouling Modeling

CFD Model. In order to investigate the effects of fouling on acompressor stage, the NASA Stage 37 test case was used as thebaseline geometry. The geometry and performance data weregathered from [16]. The entire compressor stage (rotor and stator)was simulated.

Reference Compressor Stage. The NASA Stage 37 is com-posed of a rotor and a stator. Multiple circular arc blade profileswere used in the original design for all blade rows. The overallNASA Stage 37 performance at the design point (corrected massflow of 20.19 kg/s and rotational speed of 17,188 rpm) is a pressureratio equal to 2.050 and an adiabatic efficiency equal to 0.842. Therotor is composed of 36 blades and is characterized by an inlet hub-to-tip diameter ratio of 0.7, a blade aspect ratio of 1.19, and a tip so-lidity of 1.29. The tip clearance at design speed is 0.356 mm(0.45% of the blade span). The rotor design pressure ratio and adia-batic efficiency are 2.106 and 0.877, and the design tip speed is454 m/s, respectively. The stator is composed of 46 blades. Its bladeaspect ratio is equal to 1.26 and its tip solidity is equal to 1.3.

Geometric Assumptions. To reduce computational effort,only a section of the full geometry was modeled. Due to theimpossibility of an ideal periodicity that could match both rotorand stator, the computational domain consisted of four rotorblades and five stator blades. This resulted in a 40.00� section forthe rotor and a 39.13� section for the stator. This also resulted in arotor/stator pitch ratio at the interface equal to 1.250 instead of1.278 of the real geometry.

In Fig. 1 a sketch of the computational domain is reportedThe simulations were performed in a steady multiple frame of

reference taking into account the contemporary presence of mov-ing and stationary domains by means of a mixing plane approachimposed at the rotor/stator interface (which was located halfwaybetween the two components).

Numerical Grid. The grids used in the calculations were hybridgrids generated by means of ANSYS ICEM CFD 11.0 [17]. Thegrids were realized by starting from a tetrahedral mesh and then by

Contributed by the International Gas Turbine Institute of ASME for publicationin the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript receivedJune 24, 2011; final manuscript received July 1, 2011; published online March 5,2012. Editor: Dilip R. Ballal.

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adding prism layers on the surface of the blades to help solve theboundary layer around the blade. The final mesh was composed ofabout 1,055,000 elements and nine prism layers (Fig. 1) and thefirst grid point height was fixed at 50 lm: this choice makes it pos-sible to correctly solve the boundary layers for the roughened wallin the considered range of roughness ks¼ 1–30 lm [18].

Numerical Issues. The numerical simulations were carried outwith the commercial CFD code ANSYS CFX 11.0 [19]. The codesolves the 3D Reynolds-averaged form of the Navier–Stokesequations by using a finite-element based finite-volume method.An algebraic multigrid method based on the additive correctionmultigrid strategy was used. A second-order high-resolutionadvection scheme was adopted to calculate the advection terms inthe discrete finite-volume equations.

The turbulence models used in the calculations is the standardk-e model. Near-wall effects are modeled by means of scalable wallfunctions in the k-e model, which means that the model uses empir-ical formulas that impose suitable conditions near the wall withoutresolving the boundary layer. In particular, scalable wall functionsare based on the analytical-wall-function approach (well docu-mented in [20]), in which a modified turbulent velocity scale ~us de-pendent on the turbulent kinetic energy at the near-wall node kP isused:

~us ¼ C1=4l k

1=2P (1)

and, as a consequence, a modified yþ based on ~us can be obtained:

~yþ ¼ ~usy=� (2)

The basic idea behind the scalable wall-function approach is to limitthe computed ~yþ value used in the logarithmic formulation fromfalling below 11.06, which is the value assumed for the intersectionbetween the logarithmic and the linear near wall profile [19].

In order to account for surface roughness of deteriorated blades,the near-wall model of the k-e turbulence model has to be modi-fied. For rough walls, the logarithmic profile still exists, but movescloser to the wall. As an index of the wall roughness, the equiva-lent sand grain ks is used.

Roughness effects can be accounted for by modifying the loga-rithmic profile as follows:

uþ ¼ ut

us¼ 1

jln

~yþ

1þ 0:3 � ~kþ

� �þ C (3)

where

~kþ ¼ ks ~us

�(4)

Equations (3) and (4) are coherent with the scalable wall functionsdefinition.

Boundary Conditions. The total pressure, total temperatureand flow angle were imposed at the inflow boundary. The inlettotal pressure and total temperature were fixed at p01¼ 101,325 Paand T01¼ 288.15 K, respectively.

Regarding outflow boundary conditions, two different strategieswere followed depending on the zone of the (M, b) performancemap where the working point to be simulated is located. In fact,the slope of the curve is different when near-stall or near-chokedflow regions are attained and, as a consequence, (i) an average rel-ative static pressure pr2 was imposed at the outflow boundary inthe near-choked flow region and (ii) a mass flow rate was imposedat the outflow boundary in the near-stall region.

The imposed angular velocity refers to the working conditionsat 100% design speed [16]. Therefore, the imposed rotationalspeed for the calculations was set as n¼ 17,197 rpm.

Roughness was considered uniform along the entire blade sur-face and an equivalent sand grain roughness ks value was set onthe pressure and suction surfaces of the rotor and stator blades asin Table 1. Although in real engines the surface roughness is usu-ally not uniform, it was thought that simple tests with uniformroughness will be useful in exploring the significance of surfaceroughness itself [12]. To relate Ra and ks the correlation of Kochand Smith [21] has been used, i.e., ks¼ 6.2 Ra.

Finally, since only a section of the full geometry was modeled,rotational periodic boundary conditions were applied to the lateralsurfaces of the flow domain.

Fig. 1 Modeled geometry and numerical grid for NASA Stage 37

Table 1 Parameters for simulation

ks (lm) Ra (lm) ks/c

CFD-S 1 0.16 1.77� 10�5

CFD-R1 10 1.61 1.77� 10�4

CFD-R2 15 2.42 2.66� 10�4

CFD-R3 20 3.23 3.54� 10�4

CFD-R4 25 4.03 4.43� 10�4

CFD-R5 30 4.84 5.31� 10�4

Fig. 2 Influence of fouling coefficients (cW, c/, cg) on the stagepressure coefficient curve (SF 5 0: subsonic stage)

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Model Validation. In [12], a validation of the numericalmodel was performed and confirmed that:

(i) the shapes of all the experimental performance maps is cor-rectly reproduced by the numerical code, and the errorbetween the calculated and measured values of the massflow is about 1.4% in the choked condition at 100% rota-tional speed;

(ii) the differences between the design values of the perform-ance parameters of the numerical model and the actualcompressor stage are less than 2%.

Thus, the numerical model was considered reliable.

Modification of Compressor Performance Maps Due toFouling Through the Scaling Method. The performance of afouled axial compressor stage was simulated by means of the fol-lowing equations [15]:

wp ¼ wp;max þ�wp;max � wp;FOU

� �� /wp;max

þh

SF � /wp;max� /FOU

� �� /

i2

/wp;maxþ SF � /wp;max

� /FOU

� �� /FOU

h i2(5)

wp

/2

wp

/

� �min

;wp;FOU

/FOU

� �

g ¼ gFOUþ

�gFOU � g wp=/ð Þ

min

wp;FOU

/FOU� wp

/

� �min

h i3:5

wp;FOU

/FOU

�w�p/�

� �3:5

8>>>>>>>><>>>>>>>>:

(6)

wp/ 2

wp;FOU

/FOU;

wp

/

� �max

h i

g� ¼ gFOUþ

�gFOU � g wp=/ð Þ

max

wp

/

� �max� wp;FOU

/FOU

h i2

wp

/�

wp;FOU

/FOU

� �2

8>>>>>>><>>>>>>>:

(7)

/FOU ¼ c/ � /DES

WP;FOU ¼ cW �WP;DES

gFOU ¼ cg � gDES

8><>: (8)

where cW, cu, cg [ [0,1], and cW, c/, cg¼ 1 means that the com-pressor stage is in clean conditions, while cW, cu, cg< 1 means a

Fig. 4 Comparison between literature data and IN.FO.G.T.E.calculation

Fig. 5 Fouling coefficient as function of time

Fig. 3 Influence of fouling coefficients (cW, c/, cg) on the stageefficiency curve (SF 5 20.5)

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fouled compressor stage. The coefficients cW, cu, cg depend on theoperating time, i.e.,

c/ ¼ F/ tð ÞcW ¼ FW tð Þcg ¼ Fg tð Þ

8><>: (9)

where t is the time passed since the last compressor washing; thefunctions FW(t), Fu(t), Fg(t) can be defined by a tuning procedureas better explained in [15].

Fig. 6 Comparison between the change of NASA Stage 37 performance curve (pressure coefficient versus flowcoefficient) due to fouling as evaluated by CFD method and scaling method

Table 2 Comparison between literature data and IN.FO.G.T.E.calculation

gFOU

g0

MAIR;FOU

MAIR;0

bFOU

b0

Max absolute error (%) 0.051 0.090 0.113Average error (%) �0.005 0.024 0.045Standard deviation (%) 0.028 0.048 0.049

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Equations (5) to (9) allow the calculation of pressure coeffi-cient (Wp) and the total to total isentropic efficiency (g) in the cur-rent stage conditions as a function of flow coefficient (u), shapefactor (SF), and ratio Wp/u, once the design performance (uDES,Wp,DES, and gDES) and time since the last compressor washing areknown.

Figures 2 and 3 highlight the changes of the stage pressure coef-ficient curve Wp¼FW(u, SF) and efficiency curve g¼Fg(Wp/u),

respectively, as a function of cW and cu; the Wp¼FW(u, SF) curve,in particular, refers to SF¼ 0 (subsonic stage).

In order to consider that fouling decreases moving from the firstto the last stage of a multistage compressor, the functions FcW(i),Fcu(i), and Fcg(i) were introduced. They make it possible to esti-mate coefficients cW, cu, and cg of each compressor stage as afunction of the ones of the first stage. Therefore, the performancedeterioration of the overall multistage compressor as a function of

Fig. 7 Comparison between the change of NASA Stage 37 performance curve (total to total isentropic effi-ciency versus pressure to flow coefficient ratio) due to fouling as evaluated by CFD method and scaling method

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operating hours is known if cW, cu, and cg for the first stage andFcW(i), Fcu(i), and Fcg(i) are known. More details on this scalingtechnique can be found in [15].

The tuning of the model was carried out by considering the fol-lowing trends as a function of the operating hours [22]: compres-sor efficiency (gFOU/g0), inlet mass flow rate (MAIR,FOU/MAIR,0),and pressure ratio (bFOU/b0). The tuning phase made it possible to

find, by trial and error procedure, cW, c/, and cg of the first com-pressor stage as a function of the operating hours and the func-tions FcW(i), Fcu(i), and Fcg(i) in order to reproduce the trendsreported in [22].

In Fig. 4 the comparison between literature data (continuousline) and IN.FO.G.T.E. calculations (circle and triangle markers)is presented.

The small errors and standard deviations between IN.FO.G.T.E.calculations after the tuning procedure and literature data reportedin Table 2 indicate a satisfactory calibration of the model.

Figure 5 presents cW, cu, and cg trends for the first compressorstage as a function of the operating hours as obtained by the tun-ing procedure.

It should be observed that this scaling technique makes it possi-ble to relate the change of axial stage compressor performancemaps with the machine operating hours.

Model Comparison

This section presents the comparison between the change of theaxial compressor stage performance curves due to fouling as eval-uated in [12] and [13] by CFD calculations and as calculated in[15] by means of the scaling method. More in detail, the designvalues of the flow coefficient, pressure coefficient, total to totalisentropic efficiency and shape factor were found and used in Eqs.(5) to (7) in order to fit the NASA Stage 37 performance curves inthe case of new and clean conditions (which means cW, c/,cg¼ 1). Then, the scaling technique was applied by trial and errorto determinate the number of operating hours allowing the curveto fit the performance estimated by CFD for four selected valuesof ks. The main result of this analysis is the determination of arelationship between the compressor operating hours and theincrease in the computational blade surface roughness.

Fig. 8 Equivalent sand grain roughness as function of operat-ing hours

Fig. 9 Equivalent sand grain roughness for the different compressor stages

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Figures 6 and 7 show the results of this analysis in terms of tun-ing of the scaling model with the CFD simulated performancemaps. Data gathered from CFD simulations are reported by meansof white circle markers, while the blue line represents the scaledperformance map.

As already highlighted in [12] by adding roughness to the bladesurfaces, (Wp, u) curve (Fig. 6) moves towards lower values ofboth flow and pressure coefficients. Moreover, the isentropic effi-ciency (Fig. 7) also decreases.

The generalized pressure coefficient stage performance curveperfectly fits the CFD points, both for the smooth stage and rough-ened stages. Regarding the efficiency curve, it can be highlightedthat the generalized stage performance cannot correctly representthe NASA Stage 37. The agreement between the generalizedcurve and the CFD points can only be considered satisfactoryclose to the design point. This is mainly due to the fact that thegeneralized efficiency curve was fitted to experimental measure-ments and calculated data of subsonic stages [23], while NASAStage 37 is a transonic stage [16].

Concerning the capability of the time-degradation model tocatch the reduction of the performance parameters due to theadded roughness, it can be highlighted that, also in this case, themodel perfectly fits the pressure coefficient curves. The value ofthe maximum efficiency is also correctly predicted up toks¼ 20 lm, while the scaling model overestimate the reduction ofthe maximum efficiency due to fouling for further increases. Thisis probably due to the fact that the scaling method was tuned onan axial compressor with subsonic stages [22], which may becharacterized by a different behavior when severe fouled condi-tions are achieved.

Figures 6 and 7 also report the values of the operating hoursnecessary for the stage to reach this state of degradation. This in-formation is also summarized in Fig. 8. As expected, it takes alonger time to reach higher levels of degradation (and thereforehigher values of roughness). Nevertheless, the trend is not linear:this is in accordance with the model and in particular with thefunctions in Figs. 4 and 5.

Method Application to a Multistage Compressor

The method developed has been applied to a multistage com-pressor in order to define the state of each stage in terms of com-putational roughness as a function of the operating hours. Thecompressor considered is a 17-stage axial flow compressor witha pressure ratio of about 12.5. The results are reported in Fig. 9.It can be observed that the magnitude of the added computa-tional roughness decreases in a nonlinearly manner from the firstto the last stage, while it increases by increasing the operatinghours.

In turbomachinery calculations, Koch and Smith [21] proposeda method (originally theorized by Schlichting [24]) to distinguishbetween the hydraulically smooth regime and rough regimes,based on the definition of roughness Reynolds number

Rek ¼ksW1

�(10)

where W1 is the relative inlet velocity and � is the cinematic vis-cosity of the fluid. This method states that a surface can be consid-ered hydraulically smooth when Rek is lower than 90. In the casesconsidered, this condition is verified for an equivalent sand grainks lower than 5 lm (a relative velocity W1 equal to about 300 m/scan be assumed for the first stage).

Therefore, as can be observed from Fig. 9, up to 2000 operatinghours the rough regime is verified only for the first stage. Theother stages can be considered hydraulically smooth withoutaffecting the compressor performance in a significant way. In theperspective of the computational fluid dynamics, it can beassumed that their effect is negligible, and; therefore, the rough-

ness model can only be enabled for the stages that operate in therough regime.

Conclusions

In this paper, two different approaches for the estimation of theperformance degradation of a compressor stage due to foulinghave been combined in order to understand the relationshipbetween compressor operating hours and the increase in bladecomputational surface roughness. The first approach provides theperformance changes due to fouling of an actual compressor stagethrough CFD simulations, while the second approach allows theestimation of the overall compressor performance map modifica-tion due to fouling as a function of operating hours by means of ascaling procedure.

The two methods have been applied to a compressor stage inorder to correlate the increase in the blade surface roughness withthe compressor stage operating hours.

The comparison between the two methods shows a goodmatch when the pressure coefficient curves are taken intoaccount. Regarding the efficiency curves, the agreement canonly be considered satisfactory close to the design point. This ismainly due to the fact that the generalized efficiency curve usedby the scaling procedure was fitted to experimental measure-ments and calculated data of subsonic stages, while CFD calcu-lations are performed on a transonic stage. Concerning thecapability of the time-degradation model to catch the reductionof the efficiency due to the added computational roughness, itcan be highlighted that the value of the maximum efficiency isalso correctly predicted up to an equivalent sand grain roughnessequal to 20 lm, while the scaling model overestimate efficiencyreduction for further increases.

In any case, a relation between operating the time and bladeroughness was found and applied to a multistage compressor: itwas observed that there is a significant variation in computationalroughness to be imposed in CFD simulations only after a certainamount of hours and only for the first stage.

NomenclatureC¼ constant

Cl¼ model constanth¼ total enthalpyk¼ turbulent kinetic energy

ks¼ equivalent sand grainkþ¼ nondimensional roughness height~kþ ¼ modified nondimensional roughness heightM¼ mass flow rateRa¼ center line average (CLA) roughness

Rek¼ roughness Reynolds numberSF¼ shape factor

t¼ time, hT¼ temperatureU¼ blade velocity at mean radiusut¼ velocity tangent to the wall

uþ¼ nondimensional velocity~us¼ modified friction velocity

VX¼ axial flow velocityW¼ relative velocityy¼ normal distance, Cartesian coordinate

yþ¼ nondimensional distance~yþ ¼ modified nondimensional distanceb¼ compressor or stage pressure ratioc¼ fouling scaling coefficient

/ ¼ VX

U ¼ flow coefficientj¼ model constant, Eq. (6)l¼ dynamic viscosity�¼ kinematic viscosityg¼ compressor or stage efficiency

wp ¼Dhstage

U2 ¼ pressure coefficient

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Subscripts and SuperscriptsAIR¼ airDES¼ relative to design conditionsFOU¼ relative to fouled conditions

P¼ referred to near-wall nodestage¼ compressor stage

0¼ relative to new and clean conditions*¼ normalized to design value

AcronymsCFD¼ computational fluid dynamics

IN.FO.G.T.E¼ interstage fogging gas turbine evaluation

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