The Jet Propulsion Library: Modeling and simulation of ... · The Jet Propulsion Library: Modeling and simulation of aircraft engines Michael Sielemann 1 Anand Pitchaikani 2 Nithish

The Jet Propulsion Library: Modeling and simulation of aircraftengines

Michael Sielemann1 Anand Pitchaikani2 Nithish Selvan2 Majed Sammak3

1Modelon Deutschland GmbH, Germany, [email protected] Engineering Pvt. Ltd., India, {anand.pitchaikani,nithish.selvan}@modelon.com

3Modelon AB, Sweden, [email protected]

AbstractThe Jet Propulsion Library is a new Modelica library thatprovides a foundation for modeling and simulation of jetengines, and the model-based design of integrated aircraftsystems. It provides a fully rigorous foundation for sizingand performance computations, and provides a number ofadvantages over existing domain-specific solutions due tothe use of the Modelica language. This paper provides anintroduction and overview of the library and describes anapplication in the design of a turbo fan engine.Keywords: Turbo fan, turbo jet, turbo prop, turboshaft, performance, model-based design, sizing, sec-ondary power

1 IntroductionThe prime mover of an aircraft, the jet engine, is one ofthe most important subsystem of an aircraft. Jet enginesprovide primary power (thrust) and secondary power (todrive flight control, air conditioning, cabin lighting andso on) to the aircraft. Recently, the improvements in theperformance and efficiency of jet engines deliver a verylarge share in the overall platform improvements (for bothcommercial and military aircraft where for instance supercruise requirements were met). They therefore stronglyaffect aircraft value and, in case of commercial aircraft,eventually airline competitive edge. The latter is not onlydriven by costs, but even more so by environmental regu-lations.

However, these power plant improvements become in-creasingly difficult to achieve when focusing on the en-gine in isolation. The reason is that the local improvementpotential has largely been leveraged in previous incremen-tal design improvements, and only changes on global air-craft level remain to substantially improve the total air-craft package. For this reason aeronautical systems suchas aircraft and their subsystems are becoming more andmore integrated. This integration takes place along anumber of trends. We mention two of these. The firstone is the electrification of secondary power on-board air-craft (Provost, 2002). This trend is also called the “MoreElectric Aircraft” and has shaped industry road maps sincemore than two decades. Historically, three different typesof secondary power were equal, namely, electric power,

hydraulic power, and pneumatic power. With the “MoreElectric Aircraft” this is changing in favor of electricpower. The main reason lies in the anticipated develop-ment potential of power electronics, which is all but ex-hausted (like that of pneumatic and hydraulic power).

The second trend is more recent and is the electrifica-tion of primary power. This is getting increasing interestdue to intrinsic limitations in turbofan technology (Kypri-anidis et al., 2014) (be it geared or ungeared). Follow-ing (Winter, 2013), the overall efficiency of a propulsionsystem can be considered to be proportional to the prod-uct of thermal and propulsive efficiency. To achieve ther-mal efficiency improvements, the Overall Pressure Ratio(OPR) and the Turbine Entry Temperatures (TET) of thecycles are being increased in an incremental way since thelast few decades and are approaching peak values (approx-imately 1900-2000K TET and around 45-50 cycle OPR).Material limits, turbine cooling, emissions, and losses inthe last stage of the high pressure compressor may nowimpose fundamental limits to the thermal efficiency. Im-provements in propulsive efficiency are well achievablevia reduction in fan pressure ratio and increases in by-pass ratio. However, these improvements are deterio-rated by losses through lowered transmission efficiency,increased nacelle weight and higher drag due to largerfrontal area (Larsson et al., 2011). When these limits in-deed turn out to become fundamental ones, different andmore integrated concepts will become of interest. For in-stance electric ones where power is stored in one way oranother on-board and possibly converted to electric powerby gas turbines or fuel cells and used to drive distributedpropulsion devices. Such aircraft with partially or fullyelectrified primary power systems are called hybrid orfully electric aircraft.

It is critical that the methods and tools supporting thedesign of such systems keep pace with the increasing in-tegration on the product side. Only with efficient androbust prediction capabilities it becomes possible to es-tablish model-based design for such solutions introducingnew technologies, and cover all relevant “what if” scenar-ios.

It is therefore evident that if future propulsion systemsand technology are to achieve the environmental chal-lenges and performance targets set, rigorous mathematical

DOI10.3384/ecp17132909

Proceedings of the 12th International Modelica ConferenceMay 15-17, 2017, Prague, Czech Republic

909

analysis of the component physics as well as integratedsubsystem physics is important. There exists a critical re-quirement to develop and adapt models at an appropriatelevel of fidelity to specific components. One of the key re-quirement is also to have a generic framework where theuser will be able to choose components and characteristicsof his choice before integration of the subsystem.

Given the importance of propulsion system simulationas an academic and industrial engineering discipline, theliterature on the state of the art is too extensive to bereviewed here. We therefore focus on selected refer-ences and tools. First, Gasturb (Kurzke, 1995) is a user-friendly and powerful domain-specific system simulationsoftware for gas turbines. It is mature and provides ex-tensive functionality, but also restricted to the scope de-fined by the authors. The model equations as implementedin the software can hardly be accessed and adapted bythe user. Integration with other simulation and designmodels is possible but mostly requires process integra-tion and design optimization (PIDO) solutions1. EnVi-ronmental Assessment (EVA) (Kyprianidis et al., 2008) isan example of a domain-specific simulation software withwidened scope (engine system simulation and some as-pects of aircraft sizing). Similar to Gasturb it is restrictedto the application scope envisioned by its original pro-grammers however. Numerical Propulsion System Sim-ulation (NPSS) (Nichols and Chamis, 1991; Lytle, 1999;Jones, 2007, 2010) covers more than system simulation, asit also works as integration hub between system and fieldsimulation. It can also be labeled as a domain-specificsoftware but it relies on an object-oriented (yet causal)custom language in which component models are writ-ten. Model equations as implemented can be accessed andadapted by the user. Integration can also be establishedvia PIDO solutions, but alternatively non-propulsion sub-systems can be modeled in the native NPSS language andbe integrated in a computationally more efficient and ro-bust manner than via PIDO solutions. PRopulsion Ob-ject Oriented SImulation Software (PROOSIS) (Alexiouand Mathioudakis, 2005; Bala et al., 2007) is a similarsystem simulation software. It provides the same bene-fits in terms of access and customization (albeit using anacausal language), and also allows integration using non-PIDO approaches. A number of modeling libraries fornon-propulsion sub-systems have been mentioned infor-mally but not documented in the literature (according tothe knowledge of the authors). In any case, a main limi-tation of this platform is the use of an in-house modelinglanguage, which is not widely adopted or openly standard-ized via a non-profit organization.

While connecting a wide array of tools for multi-disciplinary design optimization of aircraft and sub-

1Process Integration and Design Optimization software typicallycontains numerous CAD/CAE integration adapters that allow the userto link different computation software in a GUI. They often also pro-vide convergence, optimization, and surrogate modeling functionality,which allows to automate analysis and design processes.

systems is feasible, integrating in a less fragile way basedon open standards such as Modelica and FMI would in-crease flexibility and allowed to substantially increasemanageable problem size due to higher computational ef-ficiency. Other proposed interfacing standards such asARP 4868 (SAE, 2001) are domain specific and work wellfor model-based efforts in their respective disciplines butnot to couple analyses for unconventional designs. How-ever, up to now nobody has proposed a plausible mod-eling library in Modelica for jet engines. Such a librarycould eventually be integrated one into a framework formodeling and simulation of aircraft and their components.This enabled time and resource efficient implementationof model-based design processes via reuse of such modelassets; a key enabler for model-based design. Addition-ally, this improved consistency of results.

The objectives of this paper are

1. To suggest a library for modeling and simulation ofaircraft jet engines and their sub-systems in Model-ica for a broad range of applications ranging fromengine and sub-system conceptual design to detailedanalysis and design involving transient and real-timesimulation2.

2. To substantiate why the library can plausibly be ap-plied to industrial-scale problems involving “com-plex” models and “sophisticated” analyses

3. To apply the framework to an engineering problem,namely, the computation of the full range of cycleperformance.

4. To provide an outlook on how a Modelica imple-mentation for modeling and simulation of aircraftjet propulsion provides additional value over existingdiscipline-specific tools in the design and analysis ofunconventional systems.

2 Jet Propulsion Library: Overviewand implementation

The Jet Propulsion Library is a modeling framework forgas turbines and jet propulsion of commercial and militaryaircraft. The comprehensive set of components enablescycle performance analysis and optimization of all typesof aerospace gas turbines. On-design and off-design per-formance can be studied as well as steady-state and tran-sient behavior based on a single model.

The physics of jet engines are governed by the bal-ance equations of thermo-fluid dynamics, the conservationequations of mass, energy and momentum. Thus, some

2We restrict the scope however to only cover system simulation,i.e., all processes governed by ordinary differential equations (ODE) ordifferential-algebraic equations (DAE). Processes governed by partialdifferential equations are beyond the scope of the library, unless theirpartial derivatives have been suitably discretized to match the formalframework of an ODE or DAE (e.g., one-dimensional discretization ofthe balance equations of thermo-fluid dynamics).

The Jet Propulsion Library: Modeling and simulation of aircraft engines

910 Proceedings of the 12th International Modelica ConferenceMay 15-17, 2017, Prague, Czech Republic

DOI10.3384/ecp17132909

of the underlying principles have been documented else-where (Elmqvist et al., 2003; Casella et al., 2006; Frankeet al., 2009a,b). These will not be repeated here. How-ever, given the flow velocities in such engines some as-sumptions commonly made in the mentioned articles arenot appropriate; for instance the assumption that the flowvelocity is small and that differences between static andtotal quantities can be neglected. The following presen-tation describes some of the differences to the establishedapproaches, and gives a small example of the sophistica-tion in its implementation to address the previously men-tioned challenges.

2.1 Why ModelicaAt a first glance, domain specific simulation solutions in-cluding sophisticated graphical user interfaces are very ap-pealing. We believe however that the use of the genericmodeling language Modelica provides advantages thatmay outweigh the benefits of the former.

First, this is due to the tool support to manage productand model complexity. This relies on the object-orientednature of Modelica, and allows the tool to convenientlyfilter what implementations fit in a placeholder on a givenmodel template. Manually choosing from a large librarycan be surprisingly difficult as industrial size problems aretackled. With Modelica, models can be built rapidly basedon pre-configured templates. Additionally, a model archi-tecture can be used once implemented across the systemengineering V-cycle even as the user zooms into detailedmodeling involving dynamic and real-time analyses. Thisfacilitates creating and maintaining a holistic view even onchallenging systems.

Second, given the declarative and symbolic problemdescription encoded in the Modelica language, a modelcompiler can transform the model description (equationsystem) into the form most suitable for a given analy-sis. This is based on automatic symbolic transformations,and allows executing the same model as dynamic simula-tion, steady-state simulation, optimization, real-time sim-ulation and so on.

Additionally (and this has already been indicatedabove), using Modelica it is more straight forward to coverall domains based on first principles. After all, Modelicais one of the native languages of the aircraft sub-systemindustry. A large community/eco-system exists based onthe Modelica language with many commercial and opensource model libraries.

Furthermore, interactions become more productive.Based on the open standards, any given model can bemade available on multiple tools. This enables model-based collaborations, independently whether based onModelica or FMI.

Finally, this approach provides full access to the mod-els. After all, while complete documentation of black boxcomponent models is great for many cases, reading theactual model code including the exact equations used forsimulation in the engineering language Modelica enables

deeper understanding and customization.

2.2 Thermodynamic propertiesIn the following sections, the distinction between so-called static and total quantities is very important. A staticpressure ps for instance is the actual pressure in the usualsense, which is associated not with fluid motion but withits state. Total and dynamic pressure in turn are closelyrelated to fluid flow, and are a measure of flow veloc-ity. For incompressible fluids, Bernoulli’s equation statespt = ps + pd = ps +1/2ρv2. Here, pd = 1/2ρv2 is calledthe dynamic pressure, and pt total pressure. Total quanti-ties are sometimes also called stagnation quantities as theycorrespond to the value of the static or thermodynamicquantities if the fluid flow was brought to rest (zero veloc-ity) in a reversible way (isentropically). As we are deal-ing with compressible fluids in the context of this paper,Bernoulli’s equation does not hold. Instead, a compress-ible formulation has to be used. The details are describedin the following sections.

The thermodynamic state is always defined by the staticproperties such as static temperature and pressure. Theseare the actual temperatures and pressure observed in thereal world. In gas turbine performance computations it ishowever a tremendous simplification to express the com-ponent level equations mostly in total or stagnation quan-tities (Walsh and Fletcher, 2004). Like this, the exact flowcross section areas and velocities are not necessarily re-quired. There are however also component models, inwhich the static quantities have to be computed such asmixers and nozzles (Walsh and Fletcher, 2004). In manycases the static quantities are also of interest and are there-fore computed in the “output section” (using Modelicaparlance).

In any case, the scope of the thermodynamic propertycomputations in the Jet Propulsion Library therefore hasto cover both static and total quantities. Additionally, toensure accurate predictions, this has to be done in what iscalled the “fully rigorous” way (Kurzke, 2007). From textbooks, one is tempted use the following equation to relatethe total temperature Tt and pressure pt

Tt = Tspt

ps

γ−1γ (1)

Or, likewise

pt

ps=

(1+

γ −12

M2) γ

γ−1(2)

However, the isentropic exponent γ is not constantacross larger temperature or pressure ranges. Therefore,equations (1) and (2) are strictly speaking not applicable.Following (Kurzke, 2007; Sethi, 2008), a fully rigorousapproach based on the so-called entropy function Φ canbe used instead.

Φ(T ) =∫ T

Tre f

cp

RdTT

(3)

Session 11D: Aerospace

DOI10.3384/ecp17132909


911

Then, the change of the entropy function in an isentropicprocess is equal to the logarithm of the pressure ratio,

Φ2 −Φ1 = ln(

p2

p1

)(4)

Based on this approach, we can compute the completeset of the following six static quantities from any two ofthem plus the complete set of total quantities,

• Mass flow rate w

• Cross section area Ae

• Static pressure ps

• Static temperature Ts

• Mach Number M

• Flow velocity v

Then, instead of using (2), we can compute the staticpressure (and the complete set of static quantities) fromthe Mach Number as follows (Sethi, 2008) (note that thisprocedure requires the solution of implicit equation sys-tems and additionally the mass flow rate as input). First,we compute the static temperature Ts from the followingimplicit equation.

M =

√2ht −hs (Ts)√γs (Ts)RTs

(5)

Then, the static pressure can be computed explicitly in afully rigorous way via the following equation

ps =pt

exp(

Φt−φ(Ts)R

) (6)

As written above, the complete set of six static quan-tities can be computed from any two of them (and thetotal quantities). Based on which set of two static quan-tities is given, between zero and two numerical solutionsto implicit equations such as (5) are required to computethe full set of static quantities. Therefore, the thermody-namic properties involving rigorous computations of totaland static quantities are somewhat different to the state ofthe art in Modelica (see references above), where the needfor solution of implicit equation systems is considered arare case, which can often be avoided by suitable modelreformulations.

To provide convenient access to the computation of to-tal and static thermodynamic properties we have there-fore decided to use a package structure similar to Mod-elica.Media (Elmqvist et al., 2003) but tailored to the ap-plication specifics. First, we apply the concept of the ther-modynamic state record to both total quantities (which,following the introduction to this section, are required inall component models) and static quantities.

A typical function to compute a total thermodynamicstate record has the following interface.

replaceable partial function setTotal_pthtX"Return total state as function of pt, ht

and composition X"input AbsolutePressure pt

"Total pressure";input SpecificEnthalpy ht

"Total specific enthalpy";input MassFraction X[nS]

"Mass fractions";output TotalState total

"Total state record";end setTotal_pthtX;

Based on a given total thermodynamic state record anytotal quantity can be computed, for instance total temper-ature

TtIn = Medium.totalTemperature(inlet_total);

Additionally, a static thermodynamic state record canbe computed from a given total state record and any twoquantities related to the static quantities (w, Ae, ps, Ts,M, v as defined above). The rigorous procedure describedwith (5) and (6) is for instance implement in such a func-tion conforming to the following interface

replaceable partial function setStatic_Mnw"Return static state as function of total

state, Mach Number Mn and mass floww"

input TotalState total"Total state record";

input Real Mn"Mach Number";

input MassFlowRate w"Mass flow rate";

input Types.FlowRegime regime= Types.FlowRegime.Subsonic

"Flow velocity regime";output StaticState static

"Static state record";end setStatic_Mnw;

Enumeration FlowRegime is optionally used to con-strain the solution interval to sub-sonic, sonic, or super-sonic results.

Based on this code structuring concept fully rigor-ous thermodynamic properties are implemented in the JetPropulsion Library. See figure 1 for an overview. The un-derlying model for the entropy function and other relatedquantities can be exchanged to allow different represen-tations and fidelity levels. The first one implemented inJet Propulsion Library utilizes the polynomial approachof (Walsh and Fletcher, 2004) and does not capture disso-ciation effects.

2.3 Connector definitionFor the fluid connectors in the Jet Propulsion Librarywe adapt the concept of stream connectors as proposedin (Franke et al., 2009a,b). As defined there, the staticpressure and the static specific enthalpy are used as keyconnector variables. Given the introduction to section 2.2we instead opt for using the corresponding total quantities



DOI10.3384/ecp17132909

Figure 1. Thermodynamic property functions: Static and totalstate records plus functions acting on total state records to theleft and function acting on static state records to the right

on the connectors. Otherwise, the connector is identicalto the well-established and widely adopted fluid connec-tors. The fluid connector carries flow and thermodynamicstate information such as pressure, mass flow rate, specificenthalpy, and composition.

connector FluidPort "Fluid connector"replaceable package Medium =

GasWithCombustionProductsannotation(choicesAllMatching=true);

AbsolutePressure p"Total pressure";

flow MassFlowRate m_flow"Mass flow rate into the

component";stream SpecificEnthalpy h_outflow"Total specific enthalpy of exiting

fluid";stream MassFraction X_outflow[Medium.nS]"Mass fractions of exiting fluid";

stream ExtraProperty C_outflow[Medium.nC]"Properties c_i/m in the connection

point";end FluidPort;

Note how the Modelica naming convention is used forthe variables on the fluid connector.

Unfortunately the connector is still not directly compat-ible with libraries using the standard fluid connector (e.g.,from Modelica.Fluid) due to the use of a different pack-age structure for the computation of the thermodynamicproperties. Therefore, a simple adapter component wasrequired if connections were to be made to the high speedgas flow path models; for all other interfaces standard con-

nectors are used (fuel flow supply, shaft interfaces etc.).

2.4 Simulation modes: On-design, off-design,transient

Since the beginnings, jet engine performance computa-tions have always considered two main computation prob-lems, design point performance computation (also calledon-design performance computations) on one hand andoff-design performance computations on the other (Walshand Fletcher, 2004).

For the design point performance computation, one setof operating conditions has to be imposed. Then, the com-ponent performance levels and sizes are selected. Ad-ditionally, top level requirements are implemented (e.g.,based on cruise at altitude on an ISA day). The designpoint performance computation then allows to computeimportant cycle parameters, and to define a specific de-sign. This includes a possibly abstract or estimated enginegeometry, based on the fidelity of the analysis. Techni-cally, the output of such a design point performance com-putation are however scaling parameters on componentlevel.

Given a specific engine design (figuratively in terms ofan estimated or abstract geometry, or, more technically, interms of a complete set of component scaling parametersfor a given engine topology), the off-design performancecomputation then allows to estimate the performance atother key operating conditions (different altitude, MachNumber, day type and so on). Here geometry is fixedand operating conditions are changing. While the liter-ature typically describes off-design performance compu-tation as steady-state analysis, this may as well involvetransient simulation.

In order to provide complete functionality in relation tothe established methods, these two kinds of computationswere also implemented in the Jet Propulsion Library. Theycan be selected as “simulation modes”.

A closer look at the literature (e.g., (Walsh and Fletcher,2004)) reveals that the notion of on-design computationsis not directly compatible with the rules of balanced mod-eling in Modelica (Olsson et al., 2008). Typically, the by-pass ratio or flow split is imposed on a three-way junctionor splitter model. Following the rules of balanced mod-eling, such a component may however only impose bothdownstream pressures or impose one downstream pres-sure and the bypass ratio or a flow rate. In on-designcomputations it is however required for the scaling proce-dure to impose both downstream pressures and the bypassratio. Off-design computations in turn are basically thecomputations classically done in the Modelica language.Therefore, the corresponding simulation problems (be it insteady-state or transient mode) are fully compatible withthe concept of balanced modeling.

As the constraints of balanced modeling are imposedfor very good reasons (for instance, to improve debug-ging messages and ensure “plug and play” compatibilitywhen selecting specific implementations during system ar-


DOI10.3384/ecp17132909


913

chitecting for a given placeholder) it was not an option onthe design of the Jet Propulsion Library to rely on locallyunbalanced models. Instead, it was decided to restrict theuse of on-design computations to initial time and initialequations. Like this, initial equations are used to com-pute corresponding values of the component parametersthat have a fixed attribute equal to false. Based on this de-cision both on-design computations and off-design com-putations are in scope of the Library, and its componentand system models always remain balanced.

2.5 Component modelsWith the exception in the connector definition describedin section 2.3, the Jet Propulsion Library fully follows thevariable naming convention suggested in ARP5571 (SAE,2005).

2.5.1 Boundary conditions

The types of boundary condition models in the Jet Propul-sion Library are similar to those in other thermo-fluiddynamics libraries. Most fundamentally, we distinguishboundary conditions imposing a given mass flow rate,and boundary conditions imposing pressure (obviously allboundary conditions also impose quantities transported byconvection). These two kinds of boundary conditions arealso required for modeling and simulation of jet engines.However, the prescribed variables may now change fromon-design to off-design computations. To provide fullflexibility to the user, four different flags are exposed on aboundary condition. These allow to switch on and off theprescription of pressure and mass flow rate for on-designand off-design models respectively. To improve ease-of-use, these four flags are only exposed to the user in thecategory of advanced component parameters; normally (insimple boundary condition parameterization mode), theuser only decides whether the boundary condition is nom-inally a source or a sink.

• A nominal source prescribes both pressure and flowrate for on-design computations, and pressure for off-design computations, and

• A nominal sink prescribes neither pressure nor flowrate in on-design computation, and pressure in off-design computation.

Figure 2 shows a simple model diagram with suchboundary condition instances. Color-coding is used to il-lustrate whether a component includes over-constrainedinitial equations (nominal source with green outline) orunder-constrained initial equations (nominal sink withblue outline). As long as the number of blue componentsis equal to the number of green components the systemmodel will be well-posed (actually, any system is well-posed by construction, the color-coding still helps users todouble-check their model build-up). The color-coding isalso used on other components such as the splitter men-tioned in section 2.4 already. Quantities imposed for on-

Figure 2. Single component experiment with two boundary con-ditions (the vectorized bleed port at the top is unconnected andhas length zero)

design and off-design have the corresponding letter writ-ten in opaque font on the boundary condition, quantitiesthat are either imposed for on-design or imposed for off-design have their corresponding letter written in slightlytransparent font.

2.5.2 CompressorThe compressor model is one of the component modelsthat contains the scaling factors mentioned in section 2.4.For the compressor on-design performance computation,the user typically prescribes isentropic efficiency ηdes andpressure ratio πdes at the design point. The corrected massflow rate wc,des is not imposed directly as a parameter onthe compressor model but on the system model as a whole,and then computed from boundary conditions or inlet aswell as design bypass ratio BPRdes (the same holds for thecorrected speed Nc).

The overall compressor performance in terms of isen-tropic efficiency η (or specific work) and pressure ratioπ is encoded in performance maps (Walsh and Fletcher,2004). Based on a particular point in the performance mapthat is marked as the design point, four scaling parametersare then computed as described by (Jones, 2007).

• Is. efficiency scaling factor sη ,des =ηdes

ηdes,unscaled

• Pressure ratio scaling factor sπ,des =πdes−1

πunscaled−1

• Corrected flow scaling factor swc,des =wc,des

wc,unscaled

• Corrected speed scaling factor sNc,des =Nc,des

Nc,unscaled

Here, quantities with index unscaled indicate the valuein the original, unscaled performance map. Based on thisprocedure, one compressor map with its design point canbe scaled to represent another compressor (as described bythe target design point as prescribed by the user). As longas the design points are close enough, the scaling gives areasonable approximation of the compressor behavior.

As indicated above, the compressor model requires thatthe off-design performance is captured in the format of



DOI10.3384/ecp17132909

a performance map. The format of this performancemap has to be easy to handle in an computing environ-ment (Walsh and Fletcher, 2004), and avoid vertical orhorizontal lines in the table look-up (Jones, 2007). Forthis reason we use beta or R-line maps3. The method de-scribed by (Jones, 2007) in more detail. Basically, theperformance maps relates the important thermodynamicvariables like corrected mass flow rate, pressure ratio, cor-rected speed and the efficiency of the compressor. A com-pressor performance map using R-lines is shown in fig-ure 3. R-lines are family of curves that are parallel to thesurge line and evenly spaced among each other. The R-lines ensure unique result in the regions of low correctedair flow where pressure ratio is almost a constant and re-gions of constant air flow towards the highest air flow re-gion for a given speed line (avoiding table look-up alongvertical or horizonal tangents).

Figure 3. R-line based compressor map with speed lines (solid),r-lines (solid), and efficiency contours (dashed)

Other methods to capture the compressor performancecharacteristics are described in the literature. One exam-ple is the Map Fitting Tool (MFT) method (Sethi et al.,2013). While Jet Propulsion Library currently only im-plements the R-line or beta line methodology, the object-oriented structure allows for the convenient addition ofsuch additional map format in the future.

Once the key component performance variables wereread from the performance map, the component computa-tions continue as known from other thermo-fluid dynamicslibraries.

The compressor model also has a mechanical connec-tor through which it can receive shaft power (for instancefrom the respective turbine models).

The compressor model (like all components in the JetPropulsion Library) support the modeling of secondary airsystems. For instance, bleed can be extracted from thiscompressor model, routed through an arbitrary network,

3The notion of using an auxiliary coordinate has at least two differentnames; beta lines (Walsh and Fletcher, 2004), and R-lines (Jones, 2007).

and be supplied for turbine film cooling or for so-calledcustomer purposes. A bleed mass flow rate through thebleed ports can be specified via constant or variable bleedmass flow fractions in the model. In order to capture thestage at which the bleed air is extracted, parameter corre-sponding to the relative bleed enthalphy and the pressureas a fraction of inlet and outlet conditions are used.

2.5.3 Turbine

The turbines models are built very similar to the compres-sor models based on the off-design turbine performancemap and a set of scaling factors. For the on-design per-formance computation, the user typically prescribes isen-tropic efficiency ηdes and (uncorrected) shaft speed N atthe design point. The pressure ratio πdes, the correctedmass flow rate wc,des are again computed from boundaryconditions and the system model (the pressure ratios at thedesign point are for instance solved for such that the powerbalances per shaft are fulfilled).

The turbine performance map used is as shown in fig-ure 4. Given pressure ratio and speed, corrected flow andisentropic efficiency can be uniquely determined in a tur-bine map. This eliminates the need for R-lines as dis-cussed in the compressor section. The format is againbased on (Walsh and Fletcher, 2004; Jones, 2007). Thefour scaling parameters then computed from the perfor-mance map design point and the jet engine design pointare similar to the ones used for the compressor and de-scribed in section 2.5.2.

Figure 4. Turbine map with speed lines (solid) and efficiencycontours (dashed)

Again, once the key performance variables were readfrom the map, the component computations basicallycontinue as known from other thermo-fluid dynamics li-braries. This means for instance that the turbine modelalso has a mechanical port through which expansionpower is supplied to the compressor through shafts. Asindicated before, the turbine model optionally providesbleed ports which can receive secondary cooling air fromcompressor stages or other sources. The resulting power


DOI10.3384/ecp17132909


915

from the bleed air flows can be accounted for consideringthe tip velocity of the turbine blades.

2.5.4 InletA critical part of the inlet models are parametric predic-tions of the ram pressure recovery ηram and the spillage,bleed, and bypass drag (expressed via the correspondingdrag coefficient Cd,install). These effects can be modeledusing the correlations suggested by Kowalski (Kowalskiand Atkins, 1979). These are available in two differentflavors; a long (and more accurate) form of computationinvolving 14 tables, and a short form involving 2 com-pressed tables. The dimensional drag force due to captur-ing air Dram is eventually computed from

Dram = w · v (7)

where the ram pressure recovery ηram indirectly influencesmass flow rate. The drag force due to installation Dinstallis

Dinstall = 1/2ρv2Cd,install (8)

The given references contains more details about the im-plementation.

2.5.5 NozzleThe ideal gross thrust Fg,ideal of a nozzle can readily becomputed from the following equation

Fg,ideal = w · v+(

ps,exit − ps,amb)

Aeexit (9)

Here, ps,exit and ps,amb are the static pressures at the nozzleexit section and the ambient respectively. Again, the crui-cial question for sound model-based design application ishow much of the ideal results are achievable. This can beexpressed via a number of correlations. One of the quan-tities to use for this purpose is the nozzle exit gross thrustcoefficient CFg . This coefficient is also used by Kowal-ski (Kowalski and Atkins, 1979). Beyond CFg correlationsto approximate gross thrust Fg, this methodology also es-timates the aftbody drag coefficient Cd,ab. The former forinstance is computed based on pressure ratio and area ra-tio. Two variations for an axisymmetric nozzle as well as2-D nozzle exists. Eventually, the actual gross thrust canbe computed

Fg =CFgFg,ideal (10)

The nozzle model in the library contains replaceable mod-els to compute the contributions individually. This com-pletes the short overview of exemplary component mod-els.

2.6 Interface and template structureBased on these component models, different cycles can bebuilt up using an interface and template model structure.Different kinds of cycles such turbo fan, turbo jet, gearedturbo fan, turbo prop or turbo shaft have been disassem-bled virtually into reusable sub-system and sub-assemblymodels. Based on the object-oriented interface and tem-plate structure they can be plugged together in a highly

flexible and efficient manner. An unmixed turbo fan forinstance consists of the inlet section, fan and compres-sors, the combustor, the turbines, and the primary and sec-ondary nozzles. An exemplary break-down for such a twospool unmixed turbo fan thus is

• Inlet section

– Inlet– Inlet frame duct– Inlet engine duct

• Fan and compressor

– Fan– Splitter– Low pressure compressor– High pressure compressor– Fan duct

• Combustor

– Diffuser duct– Burner

• Turbine

– High pressure turbine– Low pressure turbine

• Primary and secondary nozzle sections

– Exhaust frame duct and exhaust tailpipe duct,or bypass exhaust frame duct

– Nozzle

Different to the state of the art described in section 1,this approach uses hierarchy and object-orientation tomanage variants and system complexity. Previous art laysall element out on a flat level. With this approach, wecan conveniently exchange inlet section models from reg-ular inlets to inlets with inlet particle separator, based onavailable map data one can conveniently switch betweenaverage and split fan models (averaging the core and by-pass fan flow, or modeling them via separate fan modelsusing different maps), number of spools, as well as de-tailed section models for compressor and turbine sections(stage representation, inclusion or removal of case strutducts, inlet guide vane ducts, transition ducts, exit guidevane ducts and so on).

An example breakdown of a turbo fan engine is illus-trated graphically in figure 5. This figure shows the actualview presented to the user in the graphical user interface ofa Modelica Integrated Development Environment (IDE).

Each type of component in the break-down above isrepresented through a class hierarchy of interfaces, tem-plates, and implementations. The implementations use theatomic components described in section 2.5.



DOI10.3384/ecp17132909

Figure 5. Top-level turbofan model breakdown shown on thetop, compressor break-down on the lower left, high pressurecompression section break-down on the lower right

3 Application example and resultsA complete jet engine model was built using the JetPropulsion Library of the Pratt & Whitney JT9D. It wascreated by configuring the two spool unmixed turbo fantemplate model. Each component starting from inlets,fans, compressors, turbines etc. is redeclared with param-eterized models. The respective performance maps areadapted from the open source distribution of the Toolboxfor the Modeling and Analysis of Thermodynamic Sys-tems (T-MATS) as described by (Chapman et al., 2014).

Table 1 provides key cycle parameters at the designpoint. These parameters are approximate but consistentwith the given source.

Table 1. Cycle design point parameters.

Parameter Value

Design point Sea level staticDay conditions ISA+15 ◦CInlet flow 698 kgs−1

Bypass ratio 5.2751Turbine inlet temperature 1260 ◦CNet thrust 223 kN

Figures 6, 7, and 8 show the compressor performancemaps. Following the principles described in section 2.5.2,these maps are scaled based on the component designpoint data given in tables 2, 3, and 4.

Table 2. Fan design point parameters.

Parameter Value

Efficiency 90.38 %Pressure ratio 1.60306

Table 3. Low pressure compressor design point parameters.

Parameter Value


Table 4. High pressure compressor design point parameters.

Parameter Value


Figure 6. JT9D fan compressor map

Figure 7. JT9D low pressure compressor map


DOI10.3384/ecp17132909


917

Figures 9 and 10 in turn show the turbine performancemaps. These maps are scaled based on the component de-sign point data given in tables 5 and 6.

Table 5. High pressure turbine design point parameters.

Parameter Value

Efficiency 91.445 %Shaft speed 8000 /min

Table 6. Low pressure turbine design point parameters.

Parameter Value

Efficiency 92.88 %Shaft speed 3750 /min

In the following, exemplary simulation results are pro-vided. For this purpose, two boundary conditions are im-posed on this model, the aircraft Mach number and thefuel flow rate. The design point simulation runs for asea-level static case. Basic sanity check results show areasonably good match of the sea level static thrust andspecific fuel consumption produced by the engine modelwith published data (Saarlas, 2007). Then, the boundarycondition parameters are varied for off-design simulation.The model was simulated to conduct a full factorial exper-iment for inputs of inlet Mach numbers (0.5, 0.7 and 0.9)and fuel flow that varied ±50% from the nominal value insteps of 5%. The results of this full factorial experiment issummarized in the two figures below.

Figure 11 plots the relationship between the low pres-sure spool speed NL and thrust for different Mach num-bers. The thrust is divided by δ = pt/pt,re f , the normal-ized inlet total pressure. The low pressure spool speed isdivided by the square root of θ = Tt/Tt,re f , the normalizedinlet total temperature. These corrections are routinelydone to normalize the data (Walsh and Fletcher, 2004).Higher Mach Numbers show lower corrected thrust due tothe inlet ram drag.

The corrected thrust specific fuel consumption trendsare shown in figure 12. Both plots are qualitatively verysimilar to the charts given in the relevant literature suchas (Walsh and Fletcher, 2004; Saarlas, 2007). Illustrativeresults of the transient simulation mode will be given in aseparate reference.

4 ConclusionsThe Jet Propulsion Library provides a foundation for mod-eling and simulation of jet engines, and the model-baseddesign of integrated aircraft system designs. It containsfully models for sizing and performance computations,and has a number of advantages over existing domain-specific solutions due to the use of the Modelica language.

Figure 8. JT9D high pressure compressor map

Figure 9. JT9D high pressure turbine map

Figure 10. JT9D low pressure turbine map



DOI10.3384/ecp17132909

Figure 11. JT9D corrected thrust vs. corrected low pressurespool speed

Figure 12. JT9D corrected thrust specific fuel consumption vs.corrected thrust

5 AcknowledgementsWe acknowledge the contributions of Shashank Swami-nathan who contributed to the interface and template struc-ture described in section 2.6 as summer intern at Modelon,Inc in 2016.

ReferencesA Alexiou and K Mathioudakis. Development of gas turbine per-

formance models using a generic simulation tool. In ASMETurbo Expo 2005: Power for Land, Sea, and Air, pages 185–194. American Society of Mechanical Engineers, 2005.

Arjun Bala, Vishal Sethi, E Lo Gatto, Vassilios Pachidis, andPericles Pilidis. ProosisUa collaborative venture for gas tur-bine performance simulation using an object oriented pro-gramming schema. In International Symposium on AirBreathing Engines, 2007.

F. Casella, M. Otter, K. Proelss, C. Richter, and H. Tummescheit.The modelica fluid and media library for modeling of incom-pressible and compressible thermo-fluid pipe networks. InProceedings of the Fifth International Modelica Conference,pages 631–640, 2006.

Jeffryes W Chapman, Thomas M Lavelle, Ryan May, Jonathan SLitt, and Ten-Huei Guo. Propulsion system simulation us-ing the toolbox for the modeling and analysis of thermody-namic systems (t mats). In 50th AIAA/ASME/SAE/ASEE JointPropulsion Conference, 2014.

Hilding Elmqvist, Hubertus Tummescheit, and Martin Otter.Object-oriented modeling of thermo-fluid systems. In PeterFritzson, editor, Proceedings of the Third International Mod-elica Conference, pages 269–286, Linköping, Sweden, 2003.

Rüdiger Franke, Francesco Casella, Martin Otter, MichaelSielemann, Sven-Erik Mattson, Hans Olsson, and HildingElmqvist. Stream connectors—an extension of Modelica fordevice-oriented modeling of convective transport phenom-ena. In Francesco Casella, editor, Proceedings of the seventhInternational Modelica conference, pages 108–121, Como,September 2009a.

Rüdiger Franke, Francesco Casella, Michael Sielemann, Ka-trin Proelss, Martin Otter, and Michael Wetter. Standard-ization of thermo-fluid modeling in Modelica.Fluid. InFrancesco Casella, editor, Proceedings of the seventh Interna-tional Modelica conference, pages 122–131, Como, Septem-ber 2009b.

Scott M Jones. An introduction to thermodynamic performanceanalysis of aircraft gas turbine engine cycles using the nu-merical propulsion system simulation code. Technical ReportTM—2007-214690, NASA, March 2007.

Scott M Jones. Steady-state modeling of gas turbine enginesusing the numerical propulsion system simulation code. InASME Turbo Expo 2010: Power for Land, Sea, and Air,pages 89–116. American Society of Mechanical Engineers,June 2010.

Edward J. Kowalski and Robert A. Atkins, Jr. A computer codefor estimating installed performance of aircraft gas turbine


DOI10.3384/ecp17132909


919

engines. Technical report, National Aeronautics and SpaceAdministration, 1979.

Joachim Kurzke. Advanced user-friendly gas turbine perfor-mance calculations on a personal computer. In ASME 1995International Gas Turbine and Aeroengine Congress and Ex-position. American Society of Mechanical Engineers, June1995.

Joachim Kurzke. About simplifications in gas turbine perfor-mance calculations. In Proceedings of the ASME Turbo Expo,volume 3, pages 14–17, May 2007.

Konstantinos G Kyprianidis, Ramon F Colmenares Quintero,Daniele S Pascovici, Stephen OT Ogaji, Pericles Pilidis, andAnestis I Kalfas. Eva: A tool for environmental assessment ofnovel propulsion cycles. In ASME Turbo Expo 2008: Powerfor Land, Sea, and Air, pages 547–556. American Society ofMechanical Engineers, 2008.

Konstantinos G Kyprianidis, Andrew M Rolt, and Tomas Grön-stedt. Multidisciplinary analysis of a geared fan intercooledcore aero-engine. Journal of Engineering for Gas Turbinesand Power, 136(1):011203, 2014.

Linda Larsson, Tomas Grönstedt, and Konstantinos G Kypriani-dis. Conceptual design and mission analysis for a geared tur-bofan and an open rotor configuration. In ASME 2011 TurboExpo: Turbine Technical Conference and Exposition, pages359–370. American Society of Mechanical Engineers, 2011.

John K Lytle. The numerical propulsion system simulation: Amultidisciplinary design system for aerospace vehicles. In In-ternational Symposium on Air Breathing Engines, September1999.

Lester Nichols and Christos Chamis. Numerical propulsionsystem simulation-an interdisciplinary approach. In Confer-ence on Advanced Space Exploration Initiative Technologies,September 1991.

Hans Olsson, Martin Otter, Sven Erik Mattsson, and HildingElmqvist. Balanced models in modelica 3.0 for increasedmodel quality. In Proceedings of the 6th International Mod-elica Conference, 2008.

Michael John Provost. The more electric aero-engine: a generaloverview from an engine manufacturer. In Power Electron-ics, Machines and Drives, 2002. International Conference on,number 487, pages 246–251. IEEE, 2002.

Maido Saarlas. Aircraft performance. John Wiley & Sons, 2007.

S-15 Gas Turbine Perf Simulation Nomenclature and InterfacesCommittee of SAE. Application programming interface re-quirements for the presentation of gas turbine engine perfor-mance on digital computers (ARP4868). Technical report,Society of Automotive Engineers, 2001.

S-15 Gas Turbine Perf Simulation Nomenclature and InterfacesCommittee of SAE. Gas turbine engine performance presen-tation and nomenclature for digital computers using object-oriented programming (ARP5571). Technical report, Societyof Automotive Engineers, 2005.

Vishal Sethi. Advanced performance simulation of gas turbinecomponents and fluid thermodynamic properties. PhD thesis,Cranfield University, April 2008.

Vishal Sethi, Georgios Doulgeris, Pericles Pilidis, Alex Nind,Marc Doussinault, Pedro Cobas, and Almudena Rueda. Themap fitting tool methodology: Gas turbine compressor off-design performance modeling. In Journal of Turbomachin-ery. American Society of Mechanical Engineers, September2013.

Philip P Walsh and Paul Fletcher. Gas turbine performance.John Wiley & Sons, 2004.

Michael Winter. A view into the next generation of commercialaviation (2025 timeframe). In AIAA Aerospace Today andTomorrow, 2013.



DOI10.3384/ecp17132909

Documents

The Jet Propulsion Library: Modeling and simulation of ... · The Jet Propulsion Library: Modeling and simulation of aircraft engines Michael Sielemann 1 Anand Pitchaikani 2 Nithish