the map fitting tool methodology: gas turbine compressor off-design performance modeling

Vishal SethiGroup Leader, TERA for Civil Aviation

e-mail: [email protected]

Georgios DoulgerisResearch Fellow

Pericles PilidisProfessor and Head of Department

Alex NindPh.D. Researcher

Department of Power and Propulsion,

School of Engineering,

Cranfield University,

Cranfield, MK430AL, UK

Marc DoussinaultResearch Program Coordinator

Snecma,

Moissy Cramayel 77550 , France

Pedro CobasHead of EcosimPro and PROOSIS

Software Development

Almudena RuedaPROOSIS Software Developer

EA Internacional,

C/ Magallanes, 1,

Madrid 28015, Spain

The Map Fitting ToolMethodology: Gas TurbineCompressor Off-DesignPerformance ModelingThis paper describes the structure and the implementation of an extended parametric rep-resentation of compressor characteristics for a modern object oriented gas turbine per-formance simulation software (PROOSIS). The proposed methodology is the map fittingtool (MFT) methodology. The proposed MFT methodology for modeling the off designperformance of gas turbine turbomachinery components (fans, compressors, and tur-bines) is based on a concept conceived and developed collaboratively by General Elec-tric (GE) and NASA. This paper provides a short description of both BETA and MFTcompressor maps, as well as the development of compressor component models inPROOSIS capable of using both types of maps for off design compressor performanceprediction. The work presented in this paper is the outcome of a collaborative effortbetween Snecma Moteurs and Cranfield University as part of the European Cycle Pro-gram of the EU FP6 collaborative project—VIVACE. A detailed description of the MFTmap methodology is provided with a “step-by-step” calculation procedure. Synergiesbetween compressor MFT and compressor BETA calculations are also highlighted and adescription of how these two components have been integrated into an object orientedsimulation software with component hierarchy is also presented. Advanced parametricrepresentations of fan and turbine characteristics have also been developed withinPROOSIS. However, a description of these methodologies is beyond the scope of thispublication. Additionally, a comparison between the advantages and disadvantagesbetween BETA and MFT maps is an interesting debate. However, this is also beyond thescope of this paper. [DOI: 10.1115/1.4023903]

Introduction

PROOSIS. The VIVACE project [1] was a European Unionintegrated project within Framework Program 6 (FP-6). The projectbegan in Jan. 2004 and concluded in Dec. 2007. VIVACE set out toaddress several of the “Vision 2020” objectives that were formu-lated by the Advisory Council for Aeronautics Research in Europe(ACARE). The main objectives of VIVACE were to achieve a 5%cost reduction in aircraft development and a 5% reduction in the de-velopment phase of a new aircraft design combined with a contri-bution to a 30% reduction in the lead time and 50% reduction indevelopment costs for a new or a derivative gas turbine [1]. Thestructure of the VIVACE project is presented in Fig. 1.

As highlighted in Fig. 1, the “VIVACE-European Cycle Program(ECP)” was part of the virtual engine subproject (SP2). The main out-come of the “VIVACE-ECP” was the development of a cost effectivegas turbine simulation environment called PROOSIS. PROOSIS[2–4], which is the Greek word for “propulsion,” is an acronym for“PRopulsion Object Oriented SImulation Software.” PROOSIS wasdeveloped by facilitating optimal use of multipartner gas turbineperformance simulation research and development resources and ex-pertise. PROOSIS is a single framework which provides shared stand-ards and methodologies for the European Union (EU) gas turbinecommunity, including original equipment manufacturers (OEMs),industrial companies, universities, and research centers.

Advanced gas turbine performance simulation software isbecoming increasingly important in design studies, mission analy-sis, life cycle analysis, performance prediction, and diagnostics.

The international gas turbine community is a multibillion poundindustry. The EU gas turbine community is a major contributor toresearch and development (R&D) of advanced gas turbine enginesand cycles for aircraft propulsion as well as land and sea basedapplications. Currently the United States of America (USA) isEurope’s biggest gas turbine technology competitor. NPSS [5,6]was developed by NASA and US based engine companies. Con-trol of NPSS has only recently transitioned from NASA to theNPSS consortium and become fully available outside the USA.NPSS is a powerful gas turbine simulation tool with severaladvanced capabilities has been used in several large projects,including the Environmental Design Space (EDS) [7–9]) project.PROOSIS, a similar tool to NPSS, encompasses advanced gas tur-bine simulation technology, which provides significant competi-tive advantages for EU partners in this highly competitiveindustry. The main advantages of PROOSIS for the EU gas tur-bine community include:

• a reduction in workload in noncompetitive areas both inter-nally and externally

• a reduction in development time and costs for all types of gasturbines or propulsion systems

• a common platform for implementing improvements inengine modeling capabilities

The PROOSIS application framework conforms to an objectoriented (OO) programming schema and fulfills the followingobject oriented criteria:

• objects• object classes• data encapsulation• inheritance and aggregation• polymorphism

Contributed by the International Gas Turbine Institute (IGTI) of ASME forpublication in the JOURNAL OF TURBOMACHINERY. Manuscript received May 11, 2011;final manuscript received January 31, 2013; published online September 13, 2013.Assoc. Editor: Aspi Wadia.

Journal of Turbomachinery NOVEMBER 2013, Vol. 135 / 061010-1Copyright VC 2013 by ASME

Downloaded From: http://turbomachinery.asmedigitalcollection.asme.org/ on 09/15/2013 Terms of Use: http://asme.org/terms

This application framework provides modularity, maintainabil-ity, reusability, and extensibility.

PROOSIS is based on the EcosimPro tool [10]. PROOSIS is asophisticated tool, which enables the user to generate mathemati-cal models of a physical system and solve the related complex nu-merical problems within the gas turbine environment. Thesemodels are programmed using a high level programming languageknown as EL. EL is an easy to learn object-oriented languagewhich was specifically developed based on the requirements of asimulation engineer as opposed to a programmer. The tool inter-nally generates Cþþ code, but this is transparent to the user. Thisphilosophy yields a powerful code with the unbeatable robustnessof Cþþ, while having complete OO capabilities. PROOSIS pro-vides an intuitive graphical user interface for modeling gas tur-bines based on a palette of component icons. The user can drag-and-drop icons into the canvas, connect them and create multipleengine configurations in an easy way. The tool will then produce amathematical model of the engine and the modeler can performmultiple calculations with this model (e.g., design and off-designcalculations, parametric studies, sensitivity analyses, etc.). Ascreenshot of the PROOSIS modeling environment is shown inFig. 2.

As a standard EU collaborative software for gas turbine per-formance simulation, one of the fundamental requirements of thesoftware was flexibility. Consequently each of the components inthe “TURBO” library (which comprises models of all the gas

turbine models) were developed with a high degree of flexibilitywith the aid of switches for selecting different calculation proce-dures (or creating user defined methodologies). A complex, yetpractical component hierarchy (with inheritance) was established.The structure of the TURBO library (at an abstract level) is shownin Fig. 3, while a detailed description of the components is givenin [11].

It was decided that two options would be provided to the userto model turbomachinery performance:

(1) the traditional BETA line (fans and compressors) andZETA line (turbine) map approaches

(2) the map fitting tool (mft) approach for fans, compressors,and turbines

Furthermore, it was decided that the code should have the flexi-bility to develop customized turbomachinery components withrespect to the number (and position) of compressor bleeds and thenumber (and position) of turbine secondary air system reintroduc-tions. Additionally a provision to simulate turbomachinery com-ponents at design point only (no maps) was also introduced. Thehierarchical structure of a wide range of compressor componentsis shown in Fig. 4. Component hierarchy is one of the several ben-efits of object oriented programming. It reduces code duplicationand redundancy thereby improving code maintainability. The pre-sented compressor hierarchy (Fig. 4) has evolved continuouslysince its conception and currently comprises a variety of

Fig. 1 Structure of the VIVACE project [1,2]

061010-2 / Vol. 135, NOVEMBER 2013 Transactions of the ASME


Fig. 2 Screenshot of the PROOSIS modeling environment showing the engine schematic canvas

Fig. 3 “TURBO” component hierarchy (abstract level)

Journal of Turbomachinery NOVEMBER 2013, Vol. 135 / 061010-3


compressor components which can be customised by the user. Adetailed description of the compressor hierarchical structure ispresented in [12]. Based on the hierarchy presented in Fig. 4, theCompressor BETA and Compressor MFT components have beenoptimally integrated to ensure that code duplication is kept to aminimum. All the common calculations of the Compressor BETAand Compressor MFT components are contained within theAbstract Components “Compressor Basic Map” and“Compressorn SasP Map” (depending on whether the user wishesto simulate a compressor with no bleeds or with a user definednumber of bleeds).

NB: “TYPE” Corresponds to Either “BETA” or “MFT”depending on the type of Compressor map. For components“Compressor(*)SasP” and “Compressor(*)SasPMapTYPE”, (*) isreplaced with an integer which corresponds to the number ofbleeds the user wishes to simulate.

This paper presents the methodology used to model the Com-pressor MFT component which is essentially an extended para-metric representation of compressor characteristics.

BETA Line Compressor Maps

This section provides a brief summary of the BETA line com-pressor map concept. The basic thermodynamic variables thatdefine the off-design performance of a gas turbine compressor areas follows:

(1) the compressor inlet corrected mass flow rate (Wc)(2) the pressure ratio of the compressor (PR)(3) the isentropic efficiency of the compressor (eff)(4) the design corrected rotational speed (NcRdes)(5) the surge pressure ratio (PRsurge)

where

(1) eff is a function of Wc and NcRdes(2) PR is a function of Wc and NcRdes(3) PRsurge is a function of Wc

The main limitation of this implementation of compressor mapsis that at high values of NcRdes, for low values of PR, the“constant speed” lines become vertical. Hence for a given valueof Wc and NcRdes, there are an infinite number of PR values.Similarly for low values of NcRdes, the “constant speed” linesbecome horizontal. Hence there are infinite values of Wc corre-sponding to fixed values of NcRdes and PR. The problem can be

solved by introducing a new auxiliary parameter called BETA.BETA serves simply as an array address and avoids the problemof horizontal and vertical portions of “constant speed” lines. Atypical Compressor BETA map is shown in Fig. 5, where

(1) Wc is a function of BETA and NcRdes(2) PR is a function of BETA and NcRdes(3) eff is a function of BETA and NcRdes(4) PRsurge is a function of Wc

A detailed description of the “inverse design” and off-designperformance of the PROOSIS Compressor BETA component ispresented in [3,12] based on the methodologies defined in [13]and explained in more detail in [14,15]. The compressor BETAmethodology will therefore not be described further here.

The Compressor Map Fitting Tool Approach

NASA and General Electric have collaboratively developed amethod called the map fitting tool (MFT) [16–18] to provide anextended parametric representation of turbomachinery maps. Thisapproach has been adopted by Snecma to model the off-designperformance of all the turbomachinery components (fans, com-pressors, and turbines) within Janus (the in-house gas turbine per-formance simulation tool developed and used by Snecma). Thedescription in this section is based on [19] which was producedfrom [16] and served as a guide for the development of Compres-sor MFT capabilities within PROOSIS.

NB: the Nomenclature used in the sections which follow (basedon the programming nomenclature used in PROOSIS) is based onthe “Aerospace Recommended Practice: Gas Turbine Engine Per-formance Presentation and Nomenclature for Digital ComputersUsing Object-Oriented Programming” [20].

Compressor MFT Component: Fundamental Definitions. Theisentropic efficiency (eff) of a compressor is defined as the ratioof the isentropic specific enthalpy rise to the real enthalpy rise ofthe compressor as shown in Eq. (1),

eff ¼Dhð Þisentropic

Dhð Þreal

(1)

where Dh is the difference between the specific enthalpy at thecompressor outlet (ht_out) and the specific enthalpy at the com-pressor inlet (ht_in) as shown in Eq. (2),

Fig. 4 Compressor MFT component hierarchy



Dh ¼ ht out-ht in (2)

The work coefficient or energy function (ghr) is defined as shownin Eq. (3),

ghr ¼ Dh

0:5� Uctip2

(3)

where Uctip is the tangential blade tip speed of the first stage ofthe compressor.

The aerodynamic loss of a compressor (gl) is defined as shownin Eq. (4),

gl ¼ ghrreal�ghrisentropic¼ghrisentropic�1

eff�1

� �(4)

Definition of Losses. For a constant value of design correctedrotational speed (NcRdes), the tangential blade tip speed (Uctip) isconstant. The corresponding “loss curve,” which is a curve of gl

Fig. 5 A typical compressor BETA line map

Fig. 6 Compressor ghr versus gl characteristic



as a function of ghr has a point of minimum loss (ml) as shown inFig. 6. At the point of minimum loss,

gl ¼ glml (5)

ghr ¼ ghml (6)

gh ¼ ghr � ghml ¼ 0 (7)

where gh is defined as the work parameter.NB, Eq. (7) is only true at the point of minimum loss (where

gl¼ glml). For all the other points on the loss characteristicgh= 0.

• For every line of “constant NcRdes” there is a point of mini-mum loss. The line which joins these minimum loss points iscalled the “backbone line.”

• For every line of “constant NcRdes,” the difference betweenthe loss at any working point and the minimum loss point(gld) is expressed as shown in Eq. (8),

gld ¼ gl� glml (8)

For a line of “constant NcRdes,” gld increases from 0 with bothan increase and a decrease in ghr as can be seen in Fig. 6.

Description of Flow. For any working point, the ratio of theaxial velocity to the tangential blade speed (VqUtip) can be definedas a function of NcRdes only. On the backbone (where gh¼ 0),the ratio of the axial velocity to tangential blade speed is referredto as VqUtipml (as it corresponds to a point of minimum loss).Even though gh¼ 0 corresponds to the minimum loss point, it

does not necessarily correspond to maximum efficiency (as willbe demonstrated in the Efficiency Calculation).

The compressor inlet Mach number (MNj) is a function of ghand NcRdesmap. For a line of “constant NcRdes,” MNj¼ 1defines the point at which the line becomes vertical.

The corrected mass flow rate (Wc) and the work parameter (gh)are limited by ghchoke which is the point at which the compressorchokes. ghchoke is a function of the NcRdesmap only. The tem-perature ratio is constant when gh <ghchoke.

Figure 7 is a graphic summary of the main flow properties high-lighted above, with respect to the choke limits for a given line of“constant NcRdes.”

Comparisons between the characteristics of Compressor BETAmaps and Compressor MFT maps are summarized in Table 1. Fig-ure 8 provides a visualization of a typical compressor MFT map.The black lines are lines of “constant gh.” The green line is the“backbone line” and corresponds to gh¼ 0 (minimum loss). Theworking line of the compressor is often close to this line. As shownin Fig. 8, the lines of “constant gh” are located on efficiency peaks.

Compressor MFT Component: Methodology. A comprehen-sive methodology for the compressor MFT approach is describedin this section. Some calculation methodologies are identical tothose for the compressor BETA component and these will behighlighted with a (*) where relevant. Calculations that applyonly to the compressor MFT methodology are marked with a (†).These calculations are included in abstract (parent) components(see Fig. 4) as they are applicable to both compressor BETA andcompressor MFT components.

Fig. 7 Compressor MFT map choke limits

Table 1 Comparison between the characteristics of compressor BETA and MFT maps

BETA map characteristics MFT map characteristics

eff as a function of (BETA and NcRdesMap) ghchoke as a function of (NcRdesMap)PR as a function of (BETA and NcRdesMap) ghml as a function of (NcRdesMap)PRsurge as a function of (Wc) gld as a function of (gh2 & NcRdesMap)Wc as a function of (BETA and NcRdesMap) glml as a function of (NcRdesMap)

MNj as a function of (gh and NcRdesMap)VqUtip as a function of (NcRdesMap)



Definition of Wc (*)

Calculation of Theta and Delta. The values of the correctedtotal temperature (theta) and the corrected total pressure (delta)are calculated using Eqs. (9) and (10), respectively,

theta ¼ Tt in

Tref

(9)

delta ¼ Pt in

Pref

(10)

where Tref is the map (BETA or MFT) reference total temperature,Pref is the map (BETA or MFT) reference total pressure, Pt_in isthe compressor inlet total pressure, Tt_in is the compressor inlettotal temperature.

NB, in general, Tref¼ Tstd¼ 288.15 K and Pref¼Pstd¼ 101 325 Pa.

Definition of Wc. The corrected mass flow rate (after applyingall scalars and adders) (wc) is defined as shown in Eq. (11),

Wc ¼ W in�ffiffiffiffiffiffiffiffiffiffithetap

delta(11)

Calculation of NcRdes (*)

Calculation of Nc. The corrected rotational speed (Nc) is cal-culated using Eq. (12),

Nc ¼ Nmechffiffiffiffiffiffiffiffiffiffithetap (12)

where Nmech is the rotational speed of the compressor.

Calculation of NcRdes. The design corrected rotational speed(NcRdes) is calculated using Eq. (13),

NcRdes ¼ Nc

NmechDesffiffiffiffiffiffiffiffiffiffithetap

� � (13)

where NmechDes is the design rotational speed of the compressor.NB, NcRdes is the design corrected rotational speed before

applying any corrections.

Obtaining Alpha (*). The value of the variable inlet guide vane(VIGV) angle or variable stator vane (VSV) angle (alpha) isobtained from a one-dimensional table of alpha versus Nmech. Thistable is input by the user as DATA and is based on a user specific“alpha law.” The value of alpha is then obtained using linearinterpolation.

Calculation of the Scalars for Gamma and Reynolds Cor-rection (*). A detailed description regarding the need for c andReynolds corrections as well as a rigorous calculation methodologyfor the scaling factors is presented in [21]. However, within PROO-SIS a simplified approach as described in [12,13] has been imple-mented. This simplified calculation methodology is presented below.

Obtaining Rref and gamref From the Fluid Model. The val-ues of map reference gas constant (Rref) and the map referenceisentropic coefficient (gamRef) are obtained from the fluid modelas shown below:

Rref is a function of FARBref and WARref

gamref is a function of Tref, FARBref, and WARref

where the values of Tref (the map reference total temperature)FARBref (the map reference burned fuel to air ratio), and WARref

(the map reference water to air ratio) are read from the MFT orBETA compressor map header.

Obtaining All the Scalars for c Correction. The four scalarsfor c correction include

– rotational speed scalar for c correction (s_gamNc)– isentropic efficiency scalar for c correction (s_gamEff)– pressure ratio scalar for c correction (s_gamPR)– corrected mass flow rate scalar for c correction (s_gamWc)

The value of each scalar is calculated as shown in Eqs.(14)–(17),

s gamNc ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffigamt in� R in

gamref � Rref

s(14)

s gamEff ¼ 1 (15)

s gamPR ¼ gamt in

gamref

(16)

s gamWc ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffigamt in� Rref

gamref � R in

s(17)

where R_in and gamt_in are obtained from the fluid model asshown below:

R_in is a function of FAR_in and WAR_ingamt_in is a function of Tt_in, FAR_in and WAR_in

Obtaining muRef From the Fluid Model and Calculation ofRNI. The value of the map reference dynamic viscosity (muRef)is obtained from the fluid model as shown below.

muRef is a function of Tref, FARBref, and WARref, where thevalues of Tref (the map reference total temperature), FARBref (themap reference burned fuel to air ratio), and WARref (the map ref-erence water to air ratio) are read from the MFT or BETA com-pressor map header.

The Reynolds number index (RNI) is calculated using Eq. (18),

RNI ¼ delta

theta

� �� muref

mut in

� �(18)

where mut_in is the compressor inlet dynamic viscosity (based on totalproperties) and is obtained from the fluid model as shown below:

mut_in is a function of Tt_in, FAR_in and WAR_in

Obtaining All the Scalars for Reynolds Correction. The twoscalars for Reynolds correction include:

– isentropic efficiency scalar for Reynolds correction (s_ReEff)– corrected mass flow rate scalar for Reynolds correction

(s_Rewc)

1. The value of each scalar is calculated as shown in Eqs. (19)and (20),

Fig. 8 Visualization of a typical compressor MFT map [19]



s ReEff ¼ logðRNIÞ � ðf 1� f 2Þ½ � þ logðRNI1Þ � f 2½ � � logðRNI2Þ � f 1½ �f g

logRNI1

RNI2

� � (19)

s ReWc ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffis ReEffp

(20)

where RNI is the Reynolds number index, RNI1 is the map refer-ence Reynolds number index 1, f1 is the map reference correctionfactor for Reynolds number index 1, RNI2 is the map referenceReynolds number index 2, f2 is the map reference correction fac-tor for Reynolds number index 2.

A good description of the need for Reynolds number correctionis given in [22] as follows: “The format of compressor and turbinemaps is based on Mach number similarity. That means that for agiven point in the map all Mach numbers in the flow field and con-sequently all losses which are a function of Mach number are im-plicitly fixed. Viscous losses, however, depend on Reynoldsnumber and therefore the values read from the maps often need tobe corrected. With high Reynolds numbers, if the boundary layeris turbulent and the surface is hydraulically rough, the Reynoldsnumber has no effect on the losses. At low Reynolds numbers,however, viscous losses are increasing and this can have a signifi-cant secondary order effect on engine performance.”

Calculation of NcRdesMap

Calculation of NcRdesMFT. The design corrected rotationalspeed (without c correction) (NcRdesMFT) is calculated byapplying a design corrected rotational speed adder and scalar tothe design corrected rotational speed (NcRdes) as shown inEq. (21),

NcRdesMFT ¼ NcRdes� a NcRdes

s NcRdes(21)

NB: Eq. (21) is expressed in the form, physical value¼ theoreticalvalue x scalarþ adder, where s_NcRdes is the design correctedrotational speed scalar, a_NcRdes is the design corrected rota-tional speed adder.

NB, for supersonic flight conditions there may be further cor-rections applied but these are not considered within the scope ofthis publication.

Calculation of NcRdesMap (*). The value of the design cor-rected rotational speed (including c correction) (NcRdesMap) iscalculated by applying the rotational speed scalar for c correction(s_gamNc) to the design corrected rotational speed (without c cor-rection) (NcRdesMFT) as shown in Eq. (22),

NcRdesMap ¼ NcRdesMFT

s gamNc(22)

As outlined in Fig. 7, NcRdesMap is a coordinate used for boththe BETA and MFT characteristics.

Calculation of ghMap (y)Obtaining the Value of ghchoke. The value of the work coeffi-

cient assuming exit annulus choked flow (ghchoke) is obtainedfrom a one-dimensional MFT map (Fig. 9). ghchoke is a functionof only the design corrected rotational speed (with c correction)(NcRdesMap).

Obtaining the Value of ghMap. The value of the work param-eter relative to MFT map conditions (ghMap) is obtained asshown in Eq. (23),

ghMap ¼ maxðgh; ghchokeÞ (23)

NB: ghMap cannot be less than ghchoke as shown in Fig. 7.NB, the variable “gh” for MFT maps is treated in a similar way

as the variable “BETA” for BETA line maps. Like BETA, gh isalso an algebraic variable. Within PROOSIS an algebraic variableis an unknown parameter, for which an initial value is provided tosolve a system of equations via an iterative process.

Calculation of effMap (y)Obtaining the value of ghmlMap. The value of the “backbone”

(minimum loss point) work coefficient (without applying a

Fig. 9 Sample “ghchoke_versus_NCRdes” characteristic



primary work coefficient scalar) (ghmlMap) is obtained from aone-dimensional MFT map (Fig. 10). ghmlMap is a function ofonly the design corrected rotational speed (with c correction)(NcRdesMap).

NB: on the “backbone line,” for any value of ghml, gh¼ 0 asindicated earlier.

Obtaining the Value of ghml. The value of the “backbone”(minimum loss point) work coefficient (including a primary workcoefficient scalar) (ghml) is calculated by applying the primarywork coefficient scalar (s_gh) to the work coefficient at the mini-mum loss point (without applying a primary work coefficient sca-lar) (ghmlMap) as shown in Eq. (24),

ghml ¼ ghmlMap� s gh (24)

The effects of s_gh¼ 1.05 (as an example) on a typical compres-sor MFT map is shown in Fig. 11.

Calculation of ghr. The work coefficient (energy function)(ghr) is the sum of the work coefficient at the minimum loss point(including a primary work coefficient scalar) (ghml) and the workcoefficient relative to MFT map conditions (ghMap) as shown inEq. (25),

ghr ¼ ghmlþ ghMap (25)

Calculation of UctipMap. The first stage tangential blade tipcorrected speed (relative to MFT map conditions) (UctipMap) isthe product of the design corrected rotational speed (with c correc-tion) (NcRdesMap) and the first stage tangential blade tip cor-rected speed at design point (UctipDes) as shown in Eq. (26),

UctipMap ¼ NcRdesMap� UctipDes (26)

where UctipDes is input by the user as DATA.

Calculation of TRmap. The temperature ratio relative to MFTmap conditions (TRmap) is calculated assuming constant specificheat. The consequence of using this assumption for compressorcalculation is described in [14,15]. The MFT map reference spe-cific heat (Cpref) and consequently the temperature ratio relativeto MFT map conditions (TRmap) are calculated using Eqs. (27)and (28), respectively,

Cpref ¼gamref � Rrefð Þ

gamref � 1ð Þ (27)

TRmap ¼UctipMap2 � ghr� �2� CpRef � Trefð Þ

þ 1 (28)

NB: the “constant specific heats” assumption is just for the pur-poses of calculating the map parameters. The overall compressorperformance is performed using the same rigorous “specific en-thalpy and entropy function” methodology which is used for thecompressor BETA component.

Obtaining the Value of glmlMap. The value of the“backbone” (minimum loss point) loss (without applying a pri-mary work coefficient scalar) (glmlMap) is obtained from a one-dimensional MFT map (Fig. 12). glmlMap is a function of onlythe design corrected rotational speed (with c correction)(NcRdesMap).

Obtaining the Value of glml. The value of the “backbone”(minimum loss point) loss (including a primary scalar) (glml) iscalculated by applying the primary loss scalar (s_gl) and the

Fig. 10 Sample “ghml_versus_NcRdes” characteristic

Fig. 11 Effects of s_gh on a typical compressor MFT map [19]



primary work coefficient scalar (s_gh) to the loss at the minimumloss point (without applying level scalars) (glmlMap) as shown inEq. (29),

glml ¼ glmlMap� s gl� s gh (29)

Calculation of gh2. The signed squared work parameter (gh2)

is the product of the work parameter (gh) and the absolute valueof the work parameter (abs(gh)) as shown in Eq. (30),

gh2 ¼ gh� absðghÞ (30)

NB: based on the definition in Eq. (30), gh2 can be negative.

Obtaining the Value of gld. The value of gld, which is the dif-ference in the loss at the working point and the minimum loss

point, is obtained from a two-dimensional MFT map (Fig. 13). gldis a function of the design corrected rotational speed (with c cor-rection) (NcRdesMap) and the signed square work parameter(gh2).

NB, gh2 is used to plot the two branches of gh as when plottedin this fashion, the loss correlation is nearly linear over a widerange of work coefficient and is therefore useful for map interpo-lation and extrapolation [16]. It can however be observed that thelosses increase quite significantly for high values of NcRdes forvalues of gh2< 0. This is a consequence of the significantdecrease in efficiency when moving away from the backbone line,in this region of the map as shown in Fig. 8.

NB, Fig. 13 only displays a range of �4 � gh2 � 4 to ease vis-ualization of the characteristic.

Calculating the Value of ghrIs. The isentropic work coeffi-cient (energy function) (ghrIs) is calculated using Eq. (31),

Fig. 12 Sample “glml_versus_NcRdes” characteristic

Fig. 13 Sample of “gld_versus_gh_NcRdes” characteristic



ghrIs ¼ ghr � glmlþ gldð Þ (31)

Calculation of effMap. The value of the isentropic efficiency(without any corrections) (effMap) is calculated using Eq. (32),

effMap ¼ ghrIs

ghr(32)

NB: for the compressor MFT components, effMap is obtainedfrom the lengthy process (as described above) by reading andinterpolating a variety of MFT characteristics. For the compressorBETA components, effMap is directly obtained from the effMapcharacteristic of the BETA line map and is simply a function ofBETA and NcRdesMap.

Calculation of effmlMap. The value of the isentropic effi-ciency at the minimum loss point / backbone (effmlMap) is calcu-lated using Eq. (33),

effmlMap ¼ 1� glmlMap� s glð ÞghmlMapð Þ

(33)

NB: effmlMap is not used by the model but is calculated just forinformation.

Calculation of the Off-Design Isentropic Efficiency (*)

Calculation of eff. The off-design isentropic efficiency (eff) isobtained by applying all the isentropic efficiency adders and sca-lars to the isentropic efficiency (without any corrections) (effMap)as shown in Eq. (34),

eff ¼ effMap� s gamEff � s ReEff � s mapEff � s adapEffð Þþ a mapEff þ a adapEffð Þ (34)

where s_gamEff is the isentropic efficiency scalar for c correction,s_ReEff is the isentropic efficiency scalar for Reynolds correction,s_mapEff is isentropic efficiency map scalar, s_adapEff is theisentropic efficiency adaptive scalar*, a_mapEff is isentropic effi-ciency map adder, a_adapEff is the isentropic efficiency adaptiveadder*.

*PROOSIS has been developed to facilitate test analysis via asuitable ANSYN (analysis by synthesis) technique. The procedureis summarized in Fig. 14.

Discrepancies between engine test bed performance and theresults obtained from both DP and OD performance simulationmodels are inevitable. The main sources of these discrepanciesare assembly or manufacturer tolerances, among others [23]. Thetest analysis process aims to minimize these discrepancies by cal-culating a series of appropriate turbo machinery map adaptive sca-lars and “calibrating” the performance simulation model based on

these scalars. A more comprehensive description of the PROOSIStest analysis capability is discussed in [24].

Calculation of PRmap (y)Calculation of TRmapIs. The isentropic temperature ratio rela-

tive to MFT map conditions (TRmapIs) is calculated as shownEq. (35),

TRmapIs ¼UctipMap2 � ghrIs� �

2� CpRef � Trefð Þ

þ 1 (35)

Calculation of PRmap. The value of pressure ratio (withoutany corrections) (PRmap) is calculated using Eq. (36),

PRmap ¼ TRmapIs gamrefð Þ= gamRef�1ð Þ½ � (36)

NB: for the compressor MFT components, PRmap is obtainedfrom the lengthy process (as it requires the value of ghrIs which isobtained by reading and interpolating a variety of MFT character-istics, as described in the previous section). For the compressorBETA components, PRmap is directly obtained from the PRmapcharacteristic of the BETA line map and is simply a function ofBETA and NcRdesMap.

Calculation of the Off-Design Pressure Ratio (*)

Calculation of PR. The off-design compressor pressure ratio(PR) is obtained by applying all the pressure ratio scalars to thepressure ratio (without any corrections) (PRmap) as shown inEq. (37),

PR ¼ absðPRmapÞs gamPR� �

� 1h i

� s mapPRn o

þ 1 (37)

where s_gamPR is the pressure ratio scalar for the c correction,and s_mapPR is the pressure ratio map scalar.

Calculation of Wcml (y)Obtaining the Value of VqUtipMap. The value of the tip axial

to tangential velocity ratio (without applying a primary scalar)(VqUtipMap) is obtained from a one-dimensional MFT map (Fig.15). VqUtipMap is a function of only the design corrected rota-tional speed (with c correction) (NcRdesMap).

Obtaining the Value of VqUtip. The value of the tip axial totangential velocity ratio (including a primary scalar) (VqUtip) iscalculated by applying the primary axial to tangential velocity ra-tio scalar (s_VqU) to the tip axial to tangential velocity ratio

Fig. 14 PROOSIS test analysis process [24] Fig. 15 Sample “VqU_versus_NcRdes” characteristic



(without applying a primary axial to tangential velocity scalar)(VqUtipMap) as shown in Eq. (38),

VqUtip ¼ VqUtipMap� s VqU (38)

Calculation of Vcml. The compressor inlet corrected velocityat the minimum loss point/backbone (Vcml) is the product of thecorrected blade tip speed (relative to MFT map conditions) (Uctip-

Map) and the axial to tangential velocity ratio (including a level 1axial to tangential velocity ratio scalar) (VqUtip) as shown inEq. (39),

Vcml ¼ UctipMap� VqUtip (39)

Calculation of Wcml. The value of the MFT map referencedensity (rhoRef) is calculated as shown in Eq. (40),

rhoRef ¼Pref

Rref � Trefð Þ (40)

The corrected mass flow rate at the minimum loss point / back-bone (Wcml) is calculated as shown in Eq. (41),

Wcml ¼ Ae� rhoRef � Vcml

� 1� Vcml2

2� Cpref � Tref

� � 1

gamRef�1ð Þ( )

(41)

where Ae is the compressor inlet effective area and is input by theuser as DATA.

Calculation of WcMap (y)Obtaining the Value of MNj. The value of the intermediate

local Mach number (MNjMap) is obtained from a two-dimensionalMFT map (Fig. 16). MNjMap is a function of the design correctedrotational speed (with c correction) (NcRdesMap) and the work pa-rameter relative to MFT map conditions (ghMap).

NB: the tabulated values include values of MNj> 1, to improveextrapolation and subsequently convergence. However, from Fig.16, it is clear that MNj cannot exceed unity.

Obtaining the Value of MNml. The value of the intermediatecompressor inlet Mach number at the minimum loss point/

“Backbone” (MNmlMap) is obtained from a two dimensionalMFT map (Fig. 16). MNmlMap is a function of the design cor-rected rotational speed (with c correction) (NcRdesMap) and thework parameter relative to MFT map conditions (ghMap), whichis set to 0 (as gh¼ 0 on the “backbone”).

NB: the compressor inlet Mach number at the minimum losspoint/“backbone” (MNml) is always less than or equal to 1.

Calculation of WcMap. The value of the corrected mass flowrate (without any corrections) (WcMap) is calculated usingEq. (42),

WcMap¼Wcml� MNj

MNml

� �

�1þ gamref �1

2

� ��MNml2

1þ gamref �1

2

� ��MNj2

8>><>>:

9>>=>>;

gamref þ1

2� gamref �1ð Þ

(42)

NB: for the compressor MFT components, WcMap is obtainedfrom the lengthy process (as described above) by reading andinterpolating a variety of MFT characteristics. For the compressorBETA components, WcMap is directly obtained from the WcMapcharacteristic of the BETA line map and is simply a function ofBETA and NcRdesMap.

Calculation of the Off-Design Corrected Mass Flow Rate(*)

Calculation of Wc. The off-design corrected mass flow rate(Wc) is obtained by applying all corrected mass flow rate addersand scalars to the corrected mass flow rate (without any correc-tions) (WcMap) as shown in Eq. (43),

IMPLðÞWc ¼ WcMap� s gamWc� s ReWc� s mapWcð�s adapWcÞ þ a mapWcþ a adapWcð Þ (43)

where s_gamWc is the corrected mass flow rate scalar for c cor-rection; s_ReWc is the corrected mass flow rate scalar for Reyn-olds correction; s_mapWc is corrected mass flow rate map scalar;s_adapWc is the corrected mass flow rate adaptive scalar *;

Fig. 16 Sample “MNj_versus_gh_NcRdes” characteristic



a_mapWc is corrected mass flow rate map adder; a_adapWc is thecorrected mass flow rate adaptive adder).

* The need for adaptive scalars and adders is presented in thesection entitled Calculation of the Off-Design Isentropic Efficiency.

NB: Wc is solved implicitly with gh as the algebraic variable forMFT maps and BETA as the algebraic variable for BETA line maps.

Calculation of the Off-Design Compressor Percentage SurgeMargin (*)

Obtaining the Value of PRsurgeMap. The value of the surgepressure ratio (without any corrections) (PRsurgeMap) is obtainedfrom a one-dimensional map. PRsurgeMap is a function of thecorrected mass flow rate (without any corrections) (WcMap) only.

NB, both MFT and BETA line maps have a “PRsurge_vs_Wc”characteristic.

Calculation of PRsurge. The off-design compressor surgepressure ratio (PRsurge) is obtained by applying all pressure ratioscalars to the surge pressure ratio (without any corrections)(PRsurgeMap) as shown in Eq. (44),

PRsurge¼ absðPRsurgeMapÞs gamPR� �

�1h i

� s mapPRn o

þ1

(44)

where s_gamPR is the pressure ratio scalar for c correction, ands_mapPR is the pressure ratio map scalar.

Calculation of SMpct. The off-design compressor percentagesurge margin (SMpct) at constant mass flow is calculated usingEq. (45),

SMpct ¼ 100� PRsurge� PRð ÞPR

(45)

NB, an analogous calculation can be performed to calculateSMpct for constant rotational speed.

Solving the System of Equations for Engine CycleCalculations. The system of equations described above is solvedby providing values of UctipDes and Ae as DATA and by provid-ing values of Nmech and gh. All the parameters can subsequentlybe calculated thereby yielding the values of Wc, eff, PR, andPRsurge.

For complete engine cycle calculations, initial (guess) values ofNmech and gh are provided and form the basis of an iterative calcu-lation to reach mass flow continuity and power balance. The con-verged solution yields the values Wc, eff, PR, and PRsurge.

Conclusion

This paper describes the structure and the implementation of anextended parametric representation of compressor characteristicsfor a modern object oriented gas turbine performance simulationsoftware (PROOSIS). The proposed methodology is the map fit-ting tool (MFT) methodology. The proposed MFT methodologyfor modeling the off design performance of gas turbine turboma-chinery components (fans, compressors, and turbines) is based ona concept conceived and developed collaboratively by GeneralElectric (GE) and NASA.

This paper provides a short description of both BETA and MFTcompressor maps, as well as the development of compressor com-ponent models in PROOSIS capable of using both types of mapsfor off design compressor performance prediction. The work pre-sented in this paper is the outcome of a collaborative effortbetween Snecma Moteurs and Cranfield University as part of theEuropean Cycle Program of the EU FP6 collaborative project,VIVACE.

A detailed description of the MFT map methodology is pro-vided with a “step-by-step” calculation procedure. Synergiesbetween compressor MFT and compressor BETA calculationsare also highlighted and a description of how these two compo-nents have been integrated into an object oriented simulationsoftware with component hierarchy is also presented. Advancedparametric representations of fan and turbine characteristicshave also been developed within PROOSIS. However a descrip-tion of these methodologies is beyond the scope of thispublication.

Acknowledgment

The authors are grateful to all the project partners involvedwithin Work Package 2.4 of the VIVACE EU FP6 Project fortheir support. The collaborative support of Snecma (SafranGroup), Empresarios Agrupados, MTU Aero Engines, AirbusFrance, ITP, Avio, Volvo Aero Corporation, Techspace Aero,Turbomeca, Iberespacio, The National Technical University ofAthens, Stuttgart University, NLR, and Cenaero is gratefullyacknowledged. The authors are also very grateful to the EuropeanUnion for financial support during the project.

Nomenclature

NB: Nomenclature used in this publication (based on the pro-gramming nomenclature used in PROOSIS) is based on the“Aerospace Recommended Practice: Gas Turbine Engine Per-formance Presentation and Nomenclature for Digital ComputersUsing Object-Oriented Programming [19].” A comprehensive no-menclature guide is provided as the nomenclature used isexhaustive.

Common Symbols for Compressor BETA

and Compressor MFT Calculations

* ¼ calculations common to both Compressor BETAand Compressor MFT methodologies

a_adapEff ¼ isentropic efficiency adaptive addera_adapWc ¼ corrected mass flow rate adaptive addera_mapEff ¼ isentropic efficiency map addera_mapWc ¼ corrected mass flow rate map addera_NcRdes ¼ design corrected rotational speed adder

alpha ¼ VIGV or VSV angle, degdelta ¼ nondimensional compressor inlet total pressure

Dh ¼ change in specific enthalpy, J/kgeff ¼ isentropic efficiency (after applying all

corrections)effMap ¼ isentropic efficiency (before applying any

corrections)f1 ¼ MFT/BETA map reference correction factor for

RNI1f2 ¼ MFT/BETA map reference correction factor for

RNI2FARref ¼ MFT/BETA map reference fuel to air ratiogamref ¼ MFT / BETA map reference isentropic coefficient

(gamma)gamt_in ¼ compressor inlet isentropic coefficient (based on

total conditions)ht_in ¼ compressor inlet specific enthalpy (based on total

conditions), J/kght_out ¼ compressor outlet specific enthalpy (based on

total conditions), J/kgmuref ¼ MFT/BETA map reference dynamic viscosity,

Ps smut_in ¼ compressor inlet dynamic viscosity (based on

total conditions), Ps sNc ¼ compressor corrected rotational speed, rpm



NcRdes ¼ design corrected rotational speed (before applyingany corrections)

NcRdesMap ¼ design corrected rotational speed (after applyingall corrections)

Nmech ¼ compressor rotational speed, rpmNmechDes ¼ compressor design rotational speed, rpm

PR ¼ pressure ratio (after applying all corrections)(including the effects of heat flux)

Pref ¼ MFT/BETA map reference pressure, PaPRmap ¼ pressure ratio (before applying any corrections)

PRsurge ¼ surge pressure ratio (after applying allcorrections)

PRsurgeMap ¼ surge pressure ratio (before applying anycorrections)

Pstd ¼ standard pressure, PaPt ¼ total pressure, Pa

R_in ¼ compressor inlet gas constant, J/(kg K)RNI ¼ Reynolds number index

RNI1 ¼ MFT/BETA map reference Reynolds numberindex 1

RNI2 ¼ MFT/BETA map reference Reynolds numberindex 2

Rref ¼ MFT/BETA map reference gas constant, J/(kg K)s_adapEff ¼ isentropic efficiency adaptive scalars_adapWc ¼ corrected mass flow rate adaptive scalars_gamEff ¼ isentropic efficiency scalar for gamma corrections_gamNc ¼ rotational speed scalar for gamma corrections_gamPR ¼ pressure ratio scalar for gamma corrections_gamWc ¼ corrected mass flow scalar for gamma corrections_mapEff ¼ isentropic efficiency map scalars_mapPR ¼ pressure ratio map scalars_mapWc ¼ corrected mass flow rate map scalars_NcRdes ¼ design corrected rotational speed scalar

s_ReEff ¼ isentropic efficiency scalar for Reynoldscorrection

s_ReWc ¼ corrected mass flow rate scalar for Reynoldscorrection

SMpct ¼ percentage surge margintheta ¼ nondimensional compressor inlet total

temperatureTref ¼ MFT/BETA map reference temperature, KTst ¼ d standard temperature, KTt ¼ total temperature, KW ¼ mass flow rate, kg/s

WARref ¼ MFT/BETA map reference water to air ratioWc ¼ corrected mass flow rate (after applying all

corrections), kg/sWcMap ¼ corrected mass flow rate (before applying any

corrections), kg/s

Specific Symbols for Compressor MFT Calculations

† ¼ calculations for Compressor MFT methodologyonly

Ae ¼ compressor inlet effective area, m2

Cpref ¼ MFT map reference specific heat, J/(kg/K)effmlMap ¼ backbone isentropic efficiency (before applying

any corrections)gh ¼ work parameter

gh2 ¼ signed square work parameterghchoke ¼ work coefficient for choked exit annulus flow

ghMap ¼ work parameter relative to MFT map conditionsghml ¼ backbone work coefficient (after applying s_gh)

ghmlMap ¼ backbone work coefficient (before applying s_gh)ghr ¼ work coefficient (also known as energy function)

ghrIs ¼ isentropic work coefficient (also known as isen-tropic energy function)

gl ¼ compressor aerodynamic lossgld ¼ difference between working point loss and

backbone loss

glml ¼ backbone loss (minimum loss) (after applyings_gl)

glmlMap ¼ backbone loss (before applying s_gl)MNj ¼ local Mach number

MNjMap ¼ intermediate local Mach numberMNml ¼ local backbone Mach number

MNmlMap ¼ intermediate local backbone Mach numberNcRdesMFT ¼ design corrected rotational speed (before applying

s_gamNc)rhoRef ¼ MFT map reference density, kg/m3

s_gh ¼ work coefficient primary scalars_gl ¼ loss primary scalar

s_VqU ¼ tip axial to tangential velocity ratio primary scalarTRmap ¼ temperature ratio relative to MFT map conditions

TRmapIs ¼ isentropic temperature ratio relative to MFT mapconditions

Uctip ¼ tangential blade tip speed of first compressorstage, m/s

UctipDes ¼ design point tangential blade tip speed, m/sUctipMap ¼ tangential blade tip speed relative to MFT map

conditions, m/sVcml ¼ compressor inlet backbone corrected velocity, m/s

VqUtip ¼ blade tip axial to tangential velocity ratio (afterapplying s_VqU)

VqUtipMap ¼ blade tip axial to tangential velocity ratio (beforeapplying s_VqU)

Wcml ¼ backbone corrected mass flow rate, kg/s

Abbreviations

ACARE ¼ Advisory Council for Aeronautics Research inEurope

ANSYN ¼ analysis by synthesisDP ¼ design point

ECP ¼ European cycle programEDS ¼ environmental design spaceMFT ¼ map fitting tool

Ml ¼ minimum lossNPSS ¼ numerical propulsion simulation software

OD ¼ off designOEM(s) ¼ original equipment manufacturer(s)

OO ¼ object orientedPROOSIS ¼ propulsion object oriented simulation software

Sas ¼ secondary air systemVIGV ¼ variable inlet guide vane (s)

VIVACE ¼ value improvement through a virtual aeronauticalcollaborative enterprise

VSV ¼ variable stator vane (s)

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the map fitting tool methodology: gas turbine compressor off-design performance modeling

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