Jeffryes W. Chapman

Vantage Partners, LLC, Brook Park, Ohio

Thomas M. Lavelle, Jonathan S. Litt, and Ten-Huei Guo

Glenn Research Center, Cleveland, Ohio

A Process for the Creation of T-MATS Propulsion 

System Models From NPSS Data

NASA/TM—2014-218409

November 2014
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Jeffryes W. Chapman

Vantage Partners, LLC, Brook Park, Ohio

Thomas M. Lavelle, Jonathan S. Litt, and Ten-Huei Guo

Glenn Research Center, Cleveland, Ohio

A Process for the Creation of T-MATS Propulsion 

System Models From NPSS Data

NASA/TM—2014-218409

November 2014

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

50th Joint Propulsion Conference

cosponsored by AIAA, ASME, SAE, and ASEE

Cleveland, Ohio, July 28–30, 2014
Acknowledgments

The authors would like to thank the NASA Aviation Safety Program’s Vehicle Systems Safety Technologies Project for funding this

work. Additionally the assistance of the NPSS team was critical in gaining a deeper understanding of the NPSS modeling process.

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Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2014-218409 1 

A Process for the Creation of T-MATS Propulsion System 

Models From NPSS Data 

Jeffryes W. Chapman 

Vantage Partners, LLC 

Brook Park, Ohio 44142 

Thomas M. Lavelle, Jonathan S. Litt, and Ten-Huei Guo 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

A modular thermodynamic simulation package called the Toolbox for the Modeling and Analysis of 

Thermodynamic Systems (T-MATS) has been developed for the creation of dynamic simulations. The 

T-MATS software is designed as a plug-in for Simulink (Math Works, Inc.) and allows a developer to 

create system simulations of thermodynamic plants (such as gas turbines) and controllers in a single tool. 

Creation of such simulations can be accomplished by matching data from actual systems, or by matching 

data from steady state models and inserting appropriate dynamics, such as the rotor and actuator dynamics 

for an aircraft engine. This paper summarizes the process for creating T-MATS turbo-machinery 

simulations using data and input files obtained from a steady state model created in the Numerical 

Propulsion System Simulation (NPSS). The NPSS is a thermodynamic simulation environment that is 

commonly used for steady state gas turbine performance analysis. Completion of all the steps involved in 

the process results in a good match between T-MATS and NPSS at several steady state operating points. 

Additionally, the T-MATS model extended to run dynamically provides the possibility of simulating and 

evaluating closed loop responses. 

Nomenclature 

Ath throat area (in.2) 

Byp_Noz bypass nozzle 

BPR Branch Pressure Ratio 

C-MAPSS40k Commercial Modular Aero-Propulsion System Simulation 40,000 lbf thrust 

C-MAPSS Commercial Modular Aero-Propulsion System Simulation 

Core_Noz core nozzle

dP change in pressure or delta pressure (psia) 

Eff efficiency 

FAR fuel to air ratio 

Fg gross thrust 

HPC high pressure compressor 

HPT high pressure turbine 

ht enthalpy 

LHV lower heating value 

LPC low pressure compressor 

LPT low pressure turbine 

N shaft speed (rpm) 
NASA/TM—2014-218409 2 

N1 low pressure shaft speed (rpm) 

N2 high pressure shaft speed (rpm) 

Nc corrected shaft speed (rpm) 

NPSS Numerical Propulsion System Simulation 

Pa ambient pressure (psia) 

PI proportional-integral 

PR pressure ratio 

Pt total pressure (psia) 

R-line uniquely defined line on the compressor map 

s_Eff map scale factor for efficiency coming from a map 

s_Nc map scale factor for corrected shaft speed going to a map 

s_PR map scale factor for pressure ratio coming from a map 

s_Wc map scale factor for corrected flow coming from a map 

T-MATS Toolbox for the Modeling and Analysis of Thermodynamic Systems 

T_std standard day temperature (518.67 qR) 

Tt total temperature (qR) 

W mass flow (pps) 

Wb bleed mass flow (pps) 

Wc corrected mass flow (pps) 

Win component input mass flow (pps) 

Subscripts: 

Des variable at the design point 

Map map variables are inputs or outputs of an empirical map model 

Perf performance variables are final modeled parameter 

I. Introduction 

In gas turbine control system design, a model is often used in place of hardware to simulate the 

system and verify controls requirements are met. This model can be obtained in many different ways. One 

such way is by developing the simulation utilizing the Numerical Propulsion System Simulation (NPSS), 

a widely used engineering modeling environment for the design and analysis of aircraft engines (Ref. 1) 

Using NPSS models can be a convenient approach because they are often created in the early stages of 

gas turbine development and they can be quite accurate, and are easily modifiable to incorporate 

additional turbine design information (Ref. 2). NPSS is a powerful gas turbine cycle modeling and 

analysis package; however, integrating NPSS models with control system models can be difficult because 

of the complexity of NPSS, which may not be compatible with the legacy codes and the simulation 

platform used in the development of the control (Ref. 3). Another approach is to use a model like 

C-MAPSS or C-MAPSS40k. Built in Simulink, C-MAPSS and C-MAPSS40k are generic commercial 

engine simulations with industry standard control architecture (Refs. 4 and 5). Controls design using a 

pre-existing generic engine with a basic controller that requires no cross platform integration can 

drastically reduce simulation setup time and allow a controls designer to test many different ideas quickly. 

However, customization of the engine model from such a tool can be difficult. 

 
NASA/TM—2014-218409 3 

To eliminate cross platform integration and allow for maximum flexibility, the Toolbox for the 

Modeling and Analysis of Thermodynamic Systems (T-MATS) can be used for gas turbine simulation 

development (Refs. 6 and 7). Written as a plug-in for MATLAB/Simulink, T-MATS contains a library of 

generic engine component models, a numerical solver, and controller blocks designed to aid in the 

creation of thermodynamic models and control systems. While T-MATS can be used to create custom 

models from engine data, legacy model data may also be leveraged for simulation generation. For 

example, the C-MAPSS simulation was re-created in T-MATS and results compared favorably within an 

acceptable error tolerance (Ref. 8). 

This paper describes a process for developing nonlinear dynamic aircraft engine simulations with 

T-MATS using information from NPSS models. Specifically, a process for leveraging maps, constants, 

and steady state data from NPSS-developed models for the creation of MATLAB/Simulink simulations 

with T-MATS. This process is demonstrated on the JT9D, a publicly available NPSS model of a dual 

spool high-bypass turbofan engine (Ref. 9). 

This process can be summarized by describing how engine component models are generated in 

T-MATS from NPSS. For components like the fan, compressors, and turbines, performance maps are 

directly utilized from NPSS. For components that are not explicitly defined, like the inlet, NPSS is run at 

a steady state point and then the inputs are perturbed to form a partial relation between the input and 

output flow variables. Nozzle performance is based on thermodynamic equations that determine static and 

total conditions at the throat and exit utilizing input parameters taken from NPSS data. For the burner, the 

fuel thermodynamic properties are included in the model, as in NPSS. The rotor dynamics are added to 

the T-MATS model using a representative rotational moment of inertia and the associated equations of 

motion, as the change in rotor speed is a function of torque differential between the turbine and 

compressor on a given rotor. Conservation of energy is ensured internally for each component, however 

mass is ensured by adding a solver that reconciles inter-component imbalances at every computation step. 

This paper will focus on the specifics of the process involved with NPSS, including extracting pertinent 

information necessary to develop the T-MATS model for the JT9D, and the model matching, which will 

be performed at takeoff and cruise to show match variation due to changes in operating point (certain 

fixed boundary conditions). Scale factors that adjust the performance of the compressor and turbine are 

determined by two methods: a data derived method that back calculates the scale factors from NPSS, and 

the T-MATS iDesign tool, which generates the scale factors based on an operating point, cruise in this 

paper. 

The paper is organized as follows. Section II offers a background on creating turbo-machinery 

simulations in T-MATS. Section III gives an overview of the procedure steps involved in this model 

development process. Section IV presents how the T-MATS simulation components and system 

architecture were selected and modified to match the NPSS model data. All model testing and results are 

detailed in Section V. Section VI describes how the simulation was converted from steady state to 

dynamic. Conclusions are discussed in Section VII. 

II. T-MATS Background 

The T-MATS software is a MATLAB plug-in that introduces additional blocks and tools to the 

Simulink environment. The turbo-machinery block set, located within T-MATS, provides access to 

parameterized gas turbine modeling components such as turbines, burners, compressors, and nozzles that 

may be used to create simulations. Turbo-machinery components are assumed to be 0-D, where the 

component-level dynamics are not modeled. Internal component calculations contain a combination of 

physics based and empirical models. Algebraic relations and component maps are used to generate 

component or system steady state solutions at specific operating points. For example, compressor 

efficiency (Eff), corrected mass flow (Wc), and pressure ratio (PR) are determined from the compressor 

map as functions of corrected shaft speed (Nc) and R-line, where R-line is an uniquely defined line on the 

compressor map. Turbine Eff and Wc are determined from the turbine map as functions of Nc and PR, 

with input cooling flow being added either at the input or output of the component. Empirical calculations 
NASA/TM—2014-218409 4 

for enthalpy and entropy are functions of temperature and pressure and are based on the assumption that 

all component mass flows consist of two compounds, air and Jet-A aircraft fuel. Physics based equations 

for turbo-machinery components in T-MATS are predominately used to calculate component energy and 

mass requirements, such as nozzle flow error. 

As stated above, a T-MATS model ensures the conservation of energy and mass. Conservation of 

energy is ensured internally to each component with energy balance equations. Although T-MATS 

ensures conservation of mass internally for some components, conservation across the system must also 

be upheld by using one of the T-MATS numerical solvers. Generally, this is done by monitoring 

conservation errors, or dependents, then using a T-MATS solver to adjust floating model variables, or 

independents, to eliminate the errors. For example, the dependent variable for a T-MATS compressor 

component is mass flow error (the difference between input mass flow and an internally calculated mass 

flow), and the independent variable is R-line. A model will be considered converged once the solver has 

updated the independents so that all dependents are at or near zero. 

While the T-MATS and NPSS environments are different, they operate in a very similar manner, in 

terms of simulating a given turbo-machinery design. Both are modular, use component maps and 

thermodynamic properties for calculations, and both require solving for system dependents by adjusting 

independents as discussed above. However, NPSS contains more flexibility in its temperature and 

pressure to enthalpy and entropy calculations, and allows for many different compound options. It should 

be noted that in this paper the JT9D engine was simulated in NPSS using air and Jet-A fuel, which are the 

same compounds as those used in T-MATS. Currently, work is being done to add alternate compound 

capability to T-MATS with the integration of the Cantera thermodynamic modeling package; however 

this is beyond the scope of this paper (Ref. 10). 

III. Process Overview 

This process assumes that a particular engine architecture has already been simulated in NPSS and 

that the cycle analysis for this design has been completed. Once the T-MATS user decides on the NPSS 

engine architecture to simulate and the respective simulation components, the following process may be 

used to create a dynamic T-MATS model from steady state NPSS data and constants. 

1. Converting maps and constants from NPSS into a useable format, while also modifying T-MATS 

components to be compatible with these maps and constants. In some cases it is necessary to 

perturb certain inputs to gain an understanding of how a component should be modeled. 

2. Completing a component level model match by taking each portion of the NPSS model and 

recreating it in T-MATS. 

3. Combining the model components into a system model with constant independent variables at the 

operating point. 

4. Creating a steady state model by integrating a solver into the system model. 

5. Converting the steady state T-MATS model to a dynamic T-MATS model. 

In the final two steps of the process, several operating points at different power levels and flight 

conditions are selected for comparison purposes. These additional tests are used to ascertain the operating 

point dependence of the model match. It should be noted that for this paper a “good” matching was 

arbitrarily chosen to be anything under a 1 percent deviation between models. In the following section, 

this procedure is demonstrated using the JT9D NPSS model. 
NASA/TM—2014-218409 5 

IV. T-MATS Simulation Creation 

Because NPSS and T-MATS are both modular it was determined that the T-MATS model would use 

the same components as the NPSS model. Figure 1 shows a block diagram detailing placement of 

components and subsequent connections, which is derived directly from NPSS module station numbers, 

shown in Appendix A. 

As mentioned above, T-MATS and NPSS are both simulations that are developed around component 

maps. For example, both simulations define compressor maps that use R-lines and Nc to generate Eff, PR, 

and Wc. For this reason, component maps were copied as they were defined in NPSS and formatted to 

insure consistency in the variable names and table structures for use in T-MATS. These reformatted maps 

can be found in Appendix B. 

Once the NPSS maps have been reformatted, it is necessary to integrate them with the T-MATS 

modeling structure using map scale factors. Map scale factors are multipliers that convert 

turbo-machinery map data to turbo-machinery performance data or vice versa and are typically used for 

shrinking or stretching a more generic model and/or converting Nc to a ratio value for map lookup. For 

this paper, map data are considered inputs or outputs of the component maps whereas performance (Perf) 

data are considered the actual values. For the creation of this T-MATS model, map scale factors were 

used to ensure a model match between NPSS and T-MATS. Shown in Table 1, for the arbitrarily chosen 

sea level static condition, are the map scale factors generated for the JT9D and the equations used to 

calculate them. Generating scale factors by deriving them from NPSS data essentially reformats the NPSS 

scale factors to be useable in T-MATS. It should be noted that there are differences between the data 

derived map scale factors in Table 1 and the map scale factors located within the NPSS data, as shown in 

Appendix A. These differences reflect variations in implementation between how T-MATS and NPSS use 

maps and scale factors. 

Figure 1.—JT9D engine component setup. 

TABLE 1.—T-MATS DATA DERIVED MAP SCALE FACTORS, CALCULATED FROM NPSS DATA 

Component Map scale 

factor 

Equation Fan LPC HPC HPT LPT 

Compressor s_Nc s_Nc = NcPerf / NcMap 3943.96 3662.66 6357.16 --------- --------- 

Turbine s_Nc s_Nc = NcPerf × 

SQRT(T_std)/NcMap 

--------- --------- --------- 34.87 18.47 

Compressor 

or Turbine 

s_Wc s_Wc = WcPerf / WcMap 0.52 0.93 0.42 0.91 0.48 

s_PR s_PR = (PRPerf-1) / (PRMap-1) 1.13 3.26 0.22 0.43 0.72 

s_Eff s_Eff = EffPerf / EffMap 0.97 0.96 1.01 0.98 1.00 
NASA/TM—2014-218409 6 

One such variation is in the turbine component equations, where NPSS and T-MATS calculate Nc 

differently. In T-MATS, Nc is referenced to a standard day temperature (T_std), while in NPSS this is not 

the case. This variation is taken into account in T-MATS by adjusting the turbine map scale factor for Nc 

(s_Nc) to include a T_std value, as shown in Table 1. It should be noted that the NPSS and T-MATS 

compressor components calculate Nc identically; therefore no additional multiplier was required for the 

compressor s_Nc definition. 

Another implementation variation between the NPSS model and T-MATS has to do with the 

inclusion of bleed flow in the Wc component of a turbine map. For instance, in T-MATS there are three 

types of corrected flows used as input to the HPT turbine component: the HPT input mass flow, cooling 

flow to the input of the HPT, and cooling flow to the output of the HPT. In T-MATS, the summation of 

the HPT input mass flow and the cooling flow to the input of the HPT is compared to the internally 

calculated Wc to generate a mass flow error, which the solver utilizes to adjust the independent variables 

accordingly. In the NPSS data, this normalized flow error is based on component input Wc only. To 

resolve this variation, the T-MATS turbine block was modified to remove the HPT input cooling flow 

from the normalized flow error calculation. This adjustment moves the bookkeeping of the cooling flow 

from the turbine component to a component downstream, and must be done only because the T-MATS 

turbine map has cooling flow included in it and the NPSS turbine map does not. 

As an alternative to using data to manually derive map scale factors for component maps, scale 

factors were also determined with the T-MATS tool iDesign. This tool is a time-saving feature that uses 

map scale factors and other key parameters to fit component maps to a design point automatically, 

effectively creating a model at a specific operating point. Map scale factors for the compressor and 

turbine may be generated by comparing the map values with performance values at a specified design 

point. Additionally, nozzle throat areas are generated by comparing nozzle mass flow at the design point 

with an internally calculated mass flow. The steady state design point selected for this study is detailed in 

Table 2, which in this case was chosen to be the cruise condition because a gas turbine is typically 

designed for this condition. Each step of the model creation process details the T-MATS model generated 

using data derived map scale factors as described earlier in this section. However, iDesign is also utilized 

during the final steps of the matching process as described in Section V. 

Additional constants required for T-MATS simulation creation are detailed in Appendix C and were 

determined from the NPSS data output located in Appendix A. The T-MATS components used for 

modeling were selected based on NPSS engine architecture, as described above, with modeling accuracy 

similar to that of the NPSS model. For example, the inlet total temperature does not change appreciably in 

the NPSS model, therefore the T-MATS model does not consider it. 

TABLE 2.—IDESIGN INPUTS FOR MAP SCALE FACTOR CALCULATION 

Component NcDesMap EffDes PRDes R-lineMap 

Fan 1.0 0.8674 1.644 2.37 

LPC 0.993 0.8685 2.485 1.7716 

HPC 0.996 0.8649 5.625 2.04 

 NcDesMap EffDes PRMap Ndes, 

rpm 

HPT 99.0 0.9132 4.934 7392 

LPT 105 0.9324 6.399 3667 

 Wdes, 

pps 

----------------- ----------------- ----------------- 

Core_Noz 113.61 ----------------- ----------------- ----------------- 

Byp_Noz 562.59 ----------------- ----------------- ----------------- 

 Altitude, 

ft 

Mach 

Number 

Temperature, 

qR 

----------------- 

Flight conditions 34000 0.8 448.43 ----------------- 
NASA/TM—2014-218409 7 

V. Model Matching 

Once the NPSS engine simulation is converted to T-MATS, model matching tests were performed 

that compared NPSS data with T-MATS generated outputs. This testing was broken down into several 

groups consisting of component level testing, system level testing without a solver, and system level 

testing with a solver. Component level tests used NPSS station data to determine how each NPSS module 

compares with its equivalent T-MATS component. The system level test without a solver brings the 

model together and validates the T-MATS component connections. For the final matching, the solver is 

enabled to verify the model will converge at the correct operating points. 

A. Component Level Testing 

A component level matching test was designed for each major part of the T-MATS JT9D high-bypass 

turbofan engine model, as detailed in Figure 1. Results from the component level testing using a takeoff 

operating point can be seen in Table 3. Stations immediately after each major engine component were 

selected for comparison purposes. Component data were gathered for the following parameters; flow (W), 

total temperature (Tt), total pressure (Pt), and gross thrust (Fg). If a parameter was not calculated at a 

particular station, either by T-MATS or NPSS, it was neglected, e.g., total pressure by the nozzle. In each 

component, the matching difference between the NPSS model and the T-MATS model was below 

0.3 percent. The largest absolute difference was in the pressure output of the low pressure compressor 

(LPC). Thrust difference was negligible for both the core bypass and core nozzles. Engine flow difference 

was below 0.1 percent in all cases. These low error values are considered to demonstrate a sufficient 

component level match. 

TABLE 3.—COMPONENT LEVEL MODEL MATCH RESULTS

Output Parameter NPSS T-MATS %Difference 

Fan 

W(pps) 1539.2 1539.21 0.0636% 

Tt(qR) 632.71 632.736 –0.0041% 

Pt(psia) 23.37 23.3669 0.0133% 

Low Pressure Compressor (LPC) 

W(pps) 245.29 245.2918 0.0743% 

Tt(qR) 821.38 822.4966 –0.1359% 

Pt(psia) 52.451 52.604 –0.2917% 

High Pressure Compressor (HPC) 

W(pps) 245.29 245.2904 0.0161% 

Tt(qR) 1398.6 1398.8 –0.0143% 

Pt(psia) 297.127 296.96 0.0562% 

High Pressure Turbine (HPT) 

W(pps) 228.18 228.1803 0.0127% 

Tt(qR) 2137.47 2136.97 0.0234% 

Pt(psia) 104.013 104.25 –0.2279% 

Low Pressure Turbine (LPT) 

W(pps) 250.25 250.25 –0.0009% 

Tt(qR) 1522.73 1522.82 –0.0059% 

Pt(psia) 22.575 22.577 –0.0089% 

Nozzle core 

W(pps) 250.25 250.251 0.0384% 

Fg(lbf) 11210 11210 0.0000% 

Nozzle bypass 

W(pps) 1293.91 1293.916 0.0495% 

Fg(lbf) 38674.8 38677.76 –0.0077% 
NASA/TM—2014-218409 8 

B. System Level Matching (Without Solver) 

Once component models are developed, they are assembled appropriately based on the engine 

architecture, shown in Figure 1, to build the engine plant model. Input flow characteristics and 

independents (e.g., R-line) are set to constants, taken from NPSS data and consistent with the takeoff 

operating point, for model match testing. These inputs consist of the values shown in Table 4. 

Table 5 shows the results from the system level test with constant inputs. It can be seen that the 

average matching differences increased significantly from those of the component level test. However, all 

differences in this test still remain well under 1 percent, with the highest difference being in nozzle W. 

Matching differences of such a low magnitude constitute a good match and it also shows that the model 

components have been connected correctly. Note in this matching step, that independents are held 

constant and the solver that insures satisfaction of conservation properties is not activated. Flow 

difference values shown in the model matching results are internal component differences and should be 

considered on a component by component basis. 

TABLE 4.—T-MATS JT9D SIMULATION INPUTS FOR SYSTEM LEVEL TESTING WITHOUT A SOLVER

TABLE 5.—MODEL MATCHING RESULTS SYSTEM LEVEL TESTING WITHOUT A SOLVER

Output Parameter NPSS T-MATS %Difference 

Fan 

W(pps) 1539.20 1542.52 0.2158% 

Tt(qR) 632.71 632.30 –0.0648% 

Pt(psia) 23.37 23.32 –0.2139% 

LPC 

W(pps) 245.29 245.82 0.2150% 

Tt(qR) 821.38 822.10 0.0877% 

Pt(psia) 52.45 52.52 0.1316% 

HPC 

W(pps) 245.29 245.52 0.0938% 

Tt(qR) 1398.60 1399.00 0.0286% 

Pt(psia) 297.13 296.60 –0.1774% 

HPT 

W(pps) 250.25 250.67 0.1680% 

Tt(qR) 2137.47 2137.00 –0.0220% 

Pt(psia) 104.01 103.80 –0.2048% 

LPT 

W(pps) 250.25 250.67 0.1682% 

Tt(qR) 1522.73 1522.00 –0.0479% 

Pt(psia) 22.58 22.54 –0.1550% 

Noz_core 

W(pps) 250.25 250.92 0.2689% 

Fg(lbf) 11210.00 11190.00 –0.1784% 

Noz_byp W(pps) 1293.91 1297.62 0.2869% 

 

Plant inputs W Pt Tt Fan 

R-line 

LPC 

R-line 

HPC 

R-line 

BPR HPT 

PR 

LPT 

PR 

N1 N2 

Value 1539.2 14.69 545.67 2.0 1.769 2.081 5.275 2.694 4.558 3750 8000 
NASA/TM—2014-218409 9 

C. System Level Matching (With Solver) 

Once the plant model is verified to have a good match, a steady state simulation is created by adding 

the T-MATS solver and connecting the system independents and dependents (Ref. 6). In this example, the 

steady state independents are system input flow (W), Fan R-line, splitter bypass ratio, LPC R-line, HPC 

R-line, HPT PR, LPT PR, N1, and N2. The steady state dependents are normalized flow differences for 

the Fan, LPC, HPC, HPT, LPT, core nozzle, and bypass nozzle, along with high and low pressure shaft 

acceleration. During simulation, the solver will drive the dependents to zero by adjusting the 

independents, effectively moving the simulation towards a new operating point. This simulation was 

performed at takeoff conditions with altitude, Mach number, and temperature, set to 0 ft, 0, and 

545.67 qR, respectively. 

Table 6 shows the results from the system level test after allowing the solver to converge with the 

scale factors developed from NPSS data as well as with scale factors created with iDesign. It can be seen 

that the matching differences from the model using NPSS-derived scale factors increase slightly from that 

of the system level test that contained constant independent variables. These differences occur due to the 

operating point moving on the map, caused by the manipulation of independents by the solver, to meet 

conservation of mass. Flow differences listed in this section take into account that each component input 

flow is matched with its component calculated flow with a difference less than 0.0001 percent. Although 

there was an increase in the difference between the models, all errors remain less than 1 percent, with the 

highest difference being the LPC pressure (Pt). The matching differences from the T-MATS model that 

utilized scale factors from the iDesign tool are generally greater in magnitude. This increase can be 

attributed to the iDesign scale factors being generated for a cruise operating point rather than the takeoff 

condition being shown below. 

TABLE 6.—MODEL MATCHING RESULTS FOR SYSTEM LEVEL TESTING WITH SOLVER 

Output Parameter NPSS T-MATS, NPSS 

scale factors 

%Difference T-MATS, 

iDesign 

%Difference 

Fan 

W(pps) 1539.20 1539.11 –0.0058% 1540.00 0.0520% 

Tt(qR) 632.71 632.78 0.0111% 632.90 0.0300% 

Pt(psia) 23.37 23.37 0.0000% 23.39 0.0685% 

LPC 

W(pps) 245.29 245.90 0.2487% 246.10 0.3302% 

Tt(qR) 821.38 823.00 0.1972% 823.30 0.2338% 

Pt(psia) 52.45 52.70 0.4747% 52.80 0.6654% 

HPC 

W(pps) 245.29 245.93 0.2593% 246.04 0.3066% 

Tt(qR) 1398.60 1401.00 0.1716% 1400.00 0.1001% 

Pt(psia) 297.13 298.00 0.2938% 298.20 0.3611% 

HPT 

W(pps) 250.25 250.90 0.2597% 251.00 0.2997% 

Tt(qR) 2137.47 2138.00 0.0248% 2139.00 0.0716% 

Pt(psia) 104.01 104.30 0.2759% 104.60 0.5644% 

LPT 

W(pps) 250.25 250.90 0.2597% 251.00 0.2997% 

Tt(qR) 1522.73 1523.00 0.0177% 1522.00 –0.0479% 

Pt(psia) 22.58 22.62 0.1993% 22.63 0.2436% 

Noz_core 

W(pps) 250.25 250.90 0.2597% 251.00 0.2997% 

Fg(lbf) 11210.00 11269.00 0.5263% 11280.00 0.6244% 

Noz_byp 

W(pps) 1293.91 1293.00 –0.0703% 1294.00 0.0070% 

Fg(lbf) 38674.80 38660.50 –0.0370% 38723.00 0.1246% 
NASA/TM—2014-218409 10 

TABLE 7.—T-MATS JT9D SIMULATION INPUTS FOR SYSTEM LEVEL TESTING 

Operating point Altitude, 

ft 

Mach Number Temperature, 

qR 

Fuel flow, 

pps 

Design point or cruise 34000.0 0.8 448.43 1.91 

Off-design point or takeoff 0.0 0.0 545.67 5.0 

TABLE 8.—T-MATS JT9D SIMULATION MATCHING RESULTS 

Simulation level Solver Operating point Scale factor derivation method Average difference 

Component No takeoff NPSS derived 0.0550% 

System No takeoff NPSS derived 0.1558% 

System Yes takeoff NPSS derived 0.1891% 

System Yes cruise NPSS derived 0.1233% 

System Yes takeoff iDesign at cruise 0.2490% 

System Yes cruise iDesign at cruise 0.0910% 

D. Model Match Testing Summary 

Up to this point, the majority of testing has been completed at the takeoff operating point with an 

engine model created by utilizing component maps and relationships developed from NPSS data or from 

the T-MATS iDesign tool. For comparison purposes, additional testing at a cruise operating point was 

also conducted. Flight conditions and fuel inputs for the takeoff and cruise operating points are listed in 

Table 7. 

To gain a general understanding of the differences generated by these methods, the magnitudes of the 

difference values for all components were averaged and then tabulated. A comparison of average 

differences is shown in Table 8. The lowest differences generated in this study were from the component 

level simulations. System level simulations completed with and without a solver and NPSS derived scale 

factors generated comparable average difference values. Running at cruise with iDesign-generated map 

scale factors, the average difference is roughly half the amount generated by the simulation using map 

scale factors derived from NPSS data. However, when scale factors generated by iDesign at cruise are 

used at the takeoff operating point the average difference roughly doubles. Although there is a large rise, 

the values are still quite low, with an average difference of less than 0.25 percent, which shows that 

calculating map scale factors by data derivation or by the T-MATS iDesign tool can lead to difference 

values of less than 1 percent at the operating points tested. 

VI. Dynamic Conversion 

Once the matching was satisfactory, the model was converted from steady state to dynamic for 

transient testing. This was accomplished by introducing integrators to calculate the shaft speeds from the 

shaft accelerations and setting up the solver discussed earlier to converge the system during each time 

step (Ref. 6). Spool moments of inertia were unavailable from the steady state NPSS model, so values 

were assumed based on engine class as detailed in Appendix C. T-MATS contains a library of control 

component blocks that can be combined to build a controller for the open-loop system (Ref. 6). In this 

example, the input fuel flow was connected to a simple proportional-integral (PI) controller based on fan 

speed. A sample run of the T-MATS dynamic simulation is shown in Figure 2. At time 15s, the fan speed 

demand is reduced by 500 rpm. It can be observed that N1, N2, gross thrust, HPC exit temperature, and 

HPC exit pressure reduce as the fuel flow is reduced. Startup transients before 5 sec are due to the system 

converging and then reaching a steady state value, and are typical with this type of simulation. Transient 

data for matching were unavailable and therefore, a direct dynamic model matching was not possible. It 

should be noted that the control system being utilized here is for demonstration purposes only; it was 

designed to adjust the fuel flow based on the fan speed error and does not take into account all of the 

operability and safety limits required in a realistic engine control design. 
NASA/TM—2014-218409 11 

Figure 2.—JT9D dynamic simulation. 

VII. Conclusion 

The T-MATS is a thermodynamic simulation system that allows developers to build custom 

thermodynamic system models within MATLAB/Simulink. The T-MATS Turbo-machinery modeling 

capability enables a user to create nonlinear steady state or dynamic gas turbine models. In creating a 

T-MATS simulation, the process described in this paper can be used to expedite the simulation 

development by leveraging NPSS data. As an example, a JT9D engine model, a publicly available dualspool high bypass gas turbine, was created from a pre-existing steady state NPSS model. The process 

consisted of selecting components, determining maps and constants, and then performing component 

level testing. This was followed by system level testing without a solver, and finally performing system 

level testing with a solver. Demonstration of this process resulted in an acceptable level of matching error 

for all operating points tested. Once a reasonable match had been achieved, the steady state simulation 

was updated in a straightforward manner by inserting appropriate dynamics, as well as a simple PI fan 

speed controller. This approach demonstrates the capability of simulating and evaluating closed loop 

responses when starting with a steady state NPSS model and that the T-MATS package provides the 

ability to convert an industry standard NPSS simulation into the user-friendly Simulink environment for 

controls development. 

 

NASA/TM—2014-218409 13 

Appendix 

A. NPSS Data Output 

*********************************************************************************************************************

Date:08/27/13 Time:10:15:44 Model: Rough JT9D Turbofan Performance Model converge = 1 CASE: 0 

Version: NPSS_2.4 Gas Package: Janaf iter/pass/Jacb/Broy= 3/ 6/ 1/ 1 Run by: tlavelle 

 

 SUMMARY OUTPUT DATA 

 MN alt dTamb W Fn TSFC Wfuel BPR VTAS OPR T4 T41 T49 

 0.000 0.0 27.00 1539.20 50012.9 0.3597 17987.64 5.2751 0.00 20.218 2730.0 2662.0 2142.4 

 core size:19.92 Q:sdfsffafd 0.00 Maximum Thrust: 0.0 % Thrust: 0.0 Power code: 0.0 

 FLOW STATION DATA 

 W Pt Tt ht FAR Wc Ps Ts Aphy MN gamt 

FS_1 Start.Fl_O 1539.20 14.696 545.67 0.30 0.0000 1578.75 14.696 545.67 -----.- 0.0000 1.39984 

FS_2 Inlet.Fl_O 1539.20 14.578 545.67 0.30 0.0000 1591.49 12.015 516.34 5944.3 0.5329 1.39984 

FS_21 Fan.Fl_O 1539.20 23.370 632.66 21.21 0.0000 1068.99 20.341 608.13 4515.2 0.4500 1.39800 

FS_13 Splitter.Fl_O2 1293.91 23.370 632.66 21.21 0.0000 898.63 20.341 608.13 3795.7 0.4500 1.39800 

FS_22 Splitter.Fl_O1 245.29 23.370 632.66 21.21 0.0000 170.35 20.341 608.13 719.5 0.4500 1.39800 

FS_23 Duct1.Fl_O 245.29 23.312 632.66 21.21 0.0000 170.78 20.290 608.13 721.4 0.4500 1.39800 

FS_24 LPC.Fl_O 245.29 52.451 821.24 66.89 0.0000 86.48 45.679 789.91 366.0 0.4500 1.39077 

FS_25 Duct2.Fl_O 245.29 52.320 821.24 66.89 0.0000 86.69 45.565 789.91 366.9 0.4500 1.39077 

FS_3 HPC.Fl_O 245.29 297.128 1398.32 212.41 0.0000 19.92 279.658 1376.22 119.9 0.3000 1.35605 

FS_36 Bld3.Fl_O 223.21 297.128 1398.32 212.41 0.0000 18.13 279.658 1376.22 109.1 0.3000 1.35605 

FS_4 Burner.Fl_O 228.21 280.786 2730.00 181.05 0.0224 27.40 279.007 2726.07 484.5 0.1000 1.28838 

FS_45 HPT.Fl_O 250.28 104.217 2142.30 41.20 0.0204 71.73 98.312 2112.97 439.0 0.3000 1.30810 

FS_48 Duct3.Fl_O 250.28 103.696 2142.35 41.20 0.0204 72.09 97.820 2113.02 441.2 0.3000 1.30810 

FS_5 LPT.Fl_O 250.28 22.748 1529.55 -132.17 0.0204 277.66 20.978 1498.73 1470.0 0.3500 1.33466 

FS_7 Duct4.Fl_O 250.28 22.521 1529.61 -132.17 0.0204 280.48 21.605 1513.77 2008.9 0.2500 1.33466 

FS_9 Core_Nozz.Fl_O 250.28 22.521 1529.67 -132.17 0.0204 280.48 14.696 1372.96 855.7 0.8193 1.33465 

FS_15 BypBld.Fl_O 1293.91 23.370 632.66 21.21 0.0000 898.63 20.341 608.13 3795.7 0.4500 1.39800 

FS_17 Duct5.Fl_O 1293.91 23.195 632.66 21.21 0.0000 905.42 20.188 608.13 3824.4 0.4500 1.39800 

FS_19 Byp_Nozz.Fl_O 1293.91 23.195 632.66 21.21 0.0000 905.42 14.696 555.46 2706.4 0.8345 1.39800 

TURBOMACHINERY PERFORMANCE DATA 

 Wc PR eff Nc TR efPoly pwr SMN SMW 

Fan 1591.49 1.603 0.9038 3656.047 1.1594 0.9100 -45538.1 27.92 16.18 

LPC 170.78 2.250 0.8658 3395.415 1.2981 0.8799 -15854.5 30.00 22.36 

HPC 86.69 5.679 0.8625 6357.714 1.7027 0.8900 -50501.1 20.00 19.97 

HPT 27.40 2.694 0.9144 153.112 1.2274 0.8987 50501.1 

LPT 72.09 4.558 0.9288 81.019 1.4009 0.9135 61391.9 

TURBOMACHINERY MAP DATA 

 WcMap PRmap effMap NcMap R/Parm s_WcDes s_PRdes s_effDes s_NcDes 

Fan 3051.46 1.420 0.9337 0.927 2.0000 0.5215 1.4369 0.9679 3943.9560 

LPC 183.19 1.383 0.9018 0.927 1.7688 0.9322 3.2631 0.9600 3662.7989 

HPC 206.12 22.630 0.8508 1.000 2.0805 0.4206 0.2163 1.0137 6357.7140 

HPT 30.15 5.000 0.9328 100.000 5.0000 1.4087 0.4236 0.9803 1.5311 

LPT 149.90 6.000 0.9276 100.000 6.0000 0.7453 0.7117 1.0013 0.8102 

===INLETS==== eRam Afs Fram 

Inlet 0.9920 -----.-- 0.0 BLEEDS - interstg Wb/Win BldWk BldP W Tt ht Pt 

 CstmrBld HPC.C> 0.0000 0.3500 0.1465 0.0000 1027.77 117.83 88.184 

====DUCTS====dPnorm MN Aphy C_LPTexit HPC.C> 0.0000 0.3500 0.1465 0.0000 1027.77 117.83 88.184 

Duct1 0.0025 0.4500 719.55 C_LPTinlt HPC.C> 0.0000 0.3500 0.1465 0.0000 1027.77 117.83 88.184 

Duct2 0.0025 0.4500 366.01 

Duct3 0.0050 0.3000 439.01 BLEEDS - output Wb/Win hscale Pscale W Tt ht Pt 

Duct4 0.0100 0.3500 1470.05 C_HPTexit Bld3.> 0.0350 1.0000 1.0000 8.5850 1398.32 212.41 297.128 

Duct5 0.0075 0.4500 3795.70 C_HPTinlt Bld3.> 0.0550 1.0000 1.0000 13.4908 1398.32 212.41 297.128 

 Duct5Lk BypBl> 0.0000 1.0000 1.0000 0.0000 632.66 21.21 23.370 

==SPLITTERS== BPR dP/P 1 dP/P 2 

Splitter 5.2751 0.0000 0.0000 

===SHAFTS==== Nmech trq in pwr in 

HP_Shaft 8000.0 33154.7 50501.1 

LP_Shaft 3750.0 85983.3 61391.9 

NASA/TM—2014-218409 15 

===BURNERS=== TtOut eff dPnorm Wfuel FAR 

Burner 2729.98 0.9940 0.0550 4.99657 0.02238 

===NOZZLES=== PR Cfg CdTh Cv Ath MNth Vact Fg 

Byp_Nozz 1.578 0.9975 1.0000 0.9975 2706.42 0.835 961.7 38674.0 

Core_Nozz 1.532 0.9999 1.0000 0.9999 855.75 0.819 1457.6 11338.9

B. T-MATS Formatted Maps 

Fan map: 

MWS.FAN.NcVec = [ 0.500 0.600 0.700 0.800 0.850 0.900 0.950... 

 1.000 1.050 1.100 1.150]; 

 MWS.FAN.RlineVec = [ 1.000 1.200 1.400 1.600 1.800... 

 2.000 2.200 2.400 2.600 2.800... 

 3.000 3.200]; 

%========== Wc = f(NcMap, RlineMap) ================== 

 MWS.FAN.WcArray = [ 1129.0825 1258.8474 1382.1909 1498.6384 1607.7749... 

 1709.2917 1802.8665 1888.3794 1965.6499 2034.6738... 

 2095.4690 2148.1226; 

 1396.9045 1546.6948 1685.6306 1813.0896 1928.5979... 

 2031.8818 2122.7800 2201.2161 2267.4148 2321.6023... 

 2364.1392 2395.5188; 

 1636.3572 1816.0977 1977.3179 2119.2051 2241.3333... 

 2343.6414 2426.3811 2490.0854 2535.5586 2563.8640... 

 2576.1626 2576.9243; 

 1884.0764 2099.0234 2284.7820 2440.4712 2565.9761... 

 2661.9326 2729.5161 2770.3828 2786.6572 2787.1653... 

 2787.1653 2787.1653; 

 2049.3005 2269.7354 2456.5759 2609.2085 2727.9202... 

 2813.8420 2868.7388 2894.8994 2898.0327 2898.0327... 

 2898.0327 2898.0327; 

 2288.3171 2492.5862 2662.3203 2797.5042 2898.9448... 

 2968.1807 3007.2944 3018.8535 3018.8535 3018.8535... 

 3018.8535 3018.8535; 

 2562.6401 2733.0469 2872.2166 2980.6609 3059.4998... 

 3110.3328 3135.1262 3138.4663 3138.4663 3138.4663... 

 3138.4663 3138.4663; 

 2769.6670 2909.9534 3022.0933 3106.9241 3165.6892... 

 3199.9995 3211.6814 3211.7039 3211.7039 3211.7039... 

 3211.7039 3211.7039; 

 2954.6721 3056.6882 3137.9358 3199.1514 3241.2805... 

 3265.4429 3272.8789 3272.8789 3272.8789 3272.8789... 

 3272.8789 3272.8789; 

 3130.1790 3195.2559 3246.9822 3285.8452 3312.4382... 

 3327.4097 3331.4949 3331.4949 3331.4949 3331.4949... 

 3331.4949 3331.4949; 

 3275.6797 3310.4507 3338.3101 3359.5127 3374.2856... 

 3382.9170 3385.6724 3385.6724 3385.6724 3385.6724... 

 3385.6724 3385.6724]; 
NASA/TM—2014-218409 16 

%========== eff = f(NcMap, RlineMap) ================== 

 MWS.FAN.EffArray = [0.7900 0.8409 0.8835 0.9160 0.9360 0.9401... 

 0.9257 0.8894 0.8233 0.7152 0.5453 0.2792 

 0.7728 0.8298 0.8776 0.9141 0.9368 0.9421... 

 0.9271 0.8885 0.8179 0.7026 0.5223 0.2425 

 0.7237 0.7965 0.8579 0.9053 0.9352 0.9432... 

 0.9256 0.8776 0.7882 0.6405 0.4067 0.0380 

 0.6854 0.7705 0.8423 0.8978 0.9331 0.9431... 

 0.9239 0.8702 0.7703 0.6058 0.3474 0.0000 

 0.7003 0.7808 0.8483 0.9001 0.9327 0.9418... 

 0.9243 0.8763 0.7882 0.6463 0.4299 0.1059 

 0.7556 0.8178 0.8692 0.9080 0.9318 0.9379... 

 0.9248 0.8907 0.8305 0.7378 0.6034 0.4147 

 0.8143 0.8549 0.8878 0.9120 0.9262 0.9290... 

 0.9201 0.8991 0.8639 0.8121 0.7405 0.6453 

 0.8431 0.8697 0.8909 0.9059 0.9142 0.9150... 

 0.9081 0.8936 0.8704 0.8373 0.7928 0.7353 

 0.8613 0.8780 0.8909 0.8998 0.9042 0.9037... 

 0.8984 0.8884 0.8731 0.8519 0.8243 0.7893 

 0.8696 0.8785 0.8851 0.8892 0.8908 0.8896... 

 0.8856 0.8791 0.8697 0.8573 0.8416 0.8222 

 0.8644 0.8680 0.8704 0.8716 0.8714 0.8699... 

 0.8670 0.8629 0.8575 0.8507 0.8424 0.8326]; 

%========== PR = f(NcMap, RlineMap) ================== 

 MWS.FAN.PRArray = [ 1.1119 1.1119 1.1098 1.1058 1.0998 1.0919... 

 1.0822 1.0711 1.0586 1.0446 1.0292 1.0125; 

 1.1622 1.1638 1.1621 1.1570 1.1487 1.1372... 

 1.1228 1.1060 1.0869 1.0655 1.0420 1.0164; 

 1.2172 1.2249 1.2266 1.2221 1.2115 1.1950... 

 1.1733 1.1471 1.1168 1.0825 1.0447 1.0035; 

 1.2858 1.3036 1.3114 1.3090 1.2965 1.2742... 

 1.2433 1.2052 1.1606 1.1099 1.0537 1.0000; 

 1.3350 1.3543 1.3628 1.3603 1.3467 1.3224... 

 1.2887 1.2474 1.1988 1.1438 1.0830 1.0174; 

 1.4075 1.4214 1.4258 1.4204 1.4055 1.3813... 

 1.3489 1.3098 1.2643 1.2131 1.1567 1.0957; 

 1.4915 1.4971 1.4955 1.4869 1.4712 1.4487... 

 1.4202 1.3867 1.3485 1.3058 1.2591 1.2086; 

 1.5579 1.5567 1.5503 1.5386 1.5218 1.5000... 

 1.4738 1.4439 1.4106 1.3739 1.3341 1.2914; 

 1.6184 1.6123 1.6024 1.5888 1.5717 1.5510... 

 1.5273 1.5010 1.4722 1.4410 1.4076 1.3720; 

 1.6748 1.6655 1.6538 1.6399 1.6238 1.6054... 

 1.5852 1.5633 1.5399 1.5150 1.4886 1.4608; 

 1.7224 1.7122 1.7008 1.6882 1.6744 1.6595... 

 1.6434 1.6266 1.6089 1.5904 1.5711 1.5510]; 

LPC map: 

MWS.LPC.NcVec = [ 0.300 0.400 0.500 0.600 0.700 0.800 0.900... 

 1.000 1.100 1.200 1.250]; 

MWS.LPC.RlineVec = [ 1.000 1.200 1.400 1.600 1.800 2.000... 

 2.200 2.400 2.600 2.800 3.000 3.200]; 
NASA/TM—2014-218409 17 

%========== Wc = f(NcMap, RlineMap) ================== 

 MWS.LPC.WcArray = [ 38.0744 42.9399 47.7510 52.5016 57.1863 61.7994... 

 66.3359 70.7905 75.1584 76.5663 76.5663 76.5663; 

 54.0383 60.0388 65.9233 71.6816 77.3038 82.7808... 

 88.1038 93.2648 98.2565 101.0545 101.0545 101.0545; 

 70.3200 77.5153 84.4949 91.2421 97.7419 103.9805... 

 109.9459 115.6273 121.0156 124.6409 124.6409 124.6409; 

 87.4860 95.6896 103.5393 111.0128 118.0907 124.7566... 

 130.9971 136.8019 142.1633 146.2312 146.2312 146.2312; 

 105.8588 114.8071 123.2285 131.0978 138.3948 145.1045... 

 151.2169 156.7268 161.6340 165.7319 165.7319 165.7319; 

 125.1164 134.6062 143.3572 151.3454 158.5548 164.9773... 

 170.6127 175.4677 179.5554 182.8951 183.0717 183.0717; 

 144.4910 154.5703 163.6243 171.6346 178.5959 184.5149... 

 189.4099 193.3090 196.2491 198.2745 198.4155 198.4155; 

 165.9141 176.2228 185.1849 192.7986 199.0806 204.0644... 

 207.7979 210.3410 211.7638 212.1506 212.1506 212.1506; 

 188.5677 198.3532 206.6834 213.5745 219.0613 223.1942... 

 226.0370 227.6647 228.1611 228.1611 228.1611 228.1611; 

 214.1402 222.1943 228.9021 234.2963 238.4220 241.3359... 

 243.1030 243.7959 243.8124 243.8124 243.8124 243.8124; 

 227.8569 234.5820 240.1193 244.5040 247.7802 250.0000... 

 251.2213 251.5216 251.5216 251.5216 251.5216 251.5216]; 

 

 

 

%========== eff = f(NcMap, RlineMap) ================== 

 MWS.LPC.EffArray = [.7256 .7656 .7978 .8195 .8274 .8164 .7494... 

 .5651 .1931 .0000 .0000 .0000; 

 .7474 .7848 .8147 .8351 .8430 .8339 .7757... 

 .6161 .3003 .0000 .0000 .0000; 

 .7610 .7984 .8286 .8496 .8586 .8516 .7977... 

 .6479 .3526 .0000 .0000 .0000; 

 .7744 .8117 .8421 .8637 .8738 .8685 .8183... 

 .6765 .3970 .0000 .0000 .0000; 

 .7872 .8240 .8542 .8759 .8866 .8827 .8360... 

 .7028 .4407 .0000 .0000 .0000; 

 .7965 .8329 .8627 .8843 .8953 .8924 .8485... 

 .7222 .4748 .0391 .0000 .0000; 

 .7997 .8368 .8673 .8896 .9013 .8991 .8561... 

 .7310 .4858 .0551 .0000 .0000; 

 .8034 .8405 .8712 .8937 .9058 .9042 .8628... 

 .7420 .5068 .0979 .0000 .0000; 

 .8214 .8533 .8793 .8981 .9079 .9062 .8724... 

 .7766 .5961 .2955 .0000 .0000; 

 .8425 .8663 .8853 .8985 .9047 .9025 .8778... 

 .8117 .6929 .5052 .2255 .0000; 

 .8540 .8731 .8880 .8981 .9024 .9000 .8800... 

 .8286 .7386 .6003 .4004 .1206]; 
NASA/TM—2014-218409 18 

%========== PR = f(NcMap, RlineMap) ================== 

 MWS.LPC.PRArray = [ 1.0423 1.0412 1.0393 1.0367 1.0333 1.0292 1.0234... 

 1.0151 1.0043 1.0000 1.0000 1.0000; 

 1.0760 1.0738 1.0704 1.0658 1.0600 1.0530 1.0434... 

 1.0297 1.0122 1.0000 1.0000 1.0000; 

 1.1215 1.1180 1.1127 1.1055 1.0965 1.0856 1.0707... 

 1.0497 1.0228 1.0000 1.0000 1.0000; 

 1.1789 1.1738 1.1660 1.1555 1.1423 1.1266 1.1052... 

 1.0753 1.0374 1.0000 1.0000 1.0000; 

 1.2494 1.2422 1.2312 1.2167 1.1986 1.1771 1.1481... 

 1.1078 1.0572 1.0000 1.0000 1.0000; 

 1.3353 1.3253 1.3105 1.2910 1.2669 1.2384 1.2002... 

 1.1476 1.0822 1.0056 1.0000 1.0000 ; 

 1.4411 1.4282 1.4088 1.3830 1.3512 1.3136 1.2632... 

 1.1942 1.1088 1.0101 1.0000 1.0000; 

 1.5724 1.5561 1.5313 1.4982 1.4572 1.4088 1.3440... 

 1.2556 1.1472 1.0233 1.0000 1.0000; 

 1.7323 1.7101 1.6785 1.6379 1.5888 1.5318 1.4572... 

 1.3572 1.2358 1.0982 1.0000 1.0000; 

 1.9360 1.9056 1.8662 1.8184 1.7625 1.6991 1.6190... 

 1.5142 1.3887 1.2471 1.0944 1.0000; 

 2.0507 2.0158 1.9729 1.9223 1.8645 1.8000 1.7201... 

 1.6176 1.4958 1.3584 1.2098 1.0546]; 

HPC map: 

 MWS.HPC.NcVec = [ 0.500 0.600 0.700 0.750 0.800 0.850 0.900 0.925 0.950 0.975... 

 1.000 1.025 1.050 ]; 

 MWS.HPC.RlineVec = [ 1.000 1.200 1.400 1.600 1.800 2.000... 

 2.200 2.400 2.600 2.800 3.000]; 

%========== Wc = f(NcMap, RlineMap) ================== 

 MWS.HPC.WcArray = [ 22.7411 24.0487 25.1548 26.0615 26.7738 27.2992... 

 27.6470 27.8286 27.8634 27.8634 27.8634; 

 31.7548 33.1181 34.2670 35.2054 35.9397 36.4783... 

 36.8308 37.0085 37.0362 37.0362 37.0362; 

 46.1066 47.4088 48.5066 49.4046 50.1096 50.6291... 

 50.9717 51.1469 51.1757 51.1757 51.1757; 

 56.7268 58.0480 59.1608 60.0704 60.7837 61.3084... 

 61.6527 61.8260 61.8517 61.8517 61.8517; 

 70.1448 71.5163 72.6688 73.6088 74.3429 74.8795... 

 75.2269 75.3943 75.4134 75.4134 75.4134; 

 89.3764 90.9746 92.3098 93.3900 94.2232 94.8199... 

 95.1897 95.3442 95.3504 95.3504 95.3504; 

 118.0620 120.1207 121.8253 123.1867 124.2166 124.9292... 

 125.3385 125.4609 125.4609 125.4609 125.4609; 

 138.5093 140.8966 142.8639 144.4238 145.5916 146.3836... 

 146.8174 146.9192 146.9192 146.9192 146.9192; 

 160.6243 162.5676 164.1805 165.4722 166.4536 167.1370... 

 167.5334 167.6563 167.6563 167.6563 167.6563; 

 181.7993 183.4993 184.9150 186.0545 186.9260 187.5389... 

 187.9029 188.0273 188.0271 188.0271 188.0271; 

 202.6315 203.5858 204.3958 205.0661 205.5998 206.0000... 

 206.2702 206.4145 206.4418 206.4418 206.4418; 

 209.9986 210.5917 211.1029 211.5321 211.8825 212.1554... 

 212.3516 212.4735 212.5220 212.5227 212.5227; 
NASA/TM—2014-218409 19 

 216.6847 217.0279 217.3287 217.5860 217.8015 217.9767... 

 218.1106 218.2041 218.2586 218.2739 218.2739]; 

 

 

 

%========== eff = f(NcMap, RlineMap) ================== 

 MWS.HPC.EffArray = [ 0.6753 0.6913 0.7016 0.7050 0.7004 0.6864 0.6570... 

 0.6044 0.5236 0.4075 0.2467; 

 0.6953 0.7094 0.7184 0.7214 0.7176 0.7058 0.6812... 

 0.6378 0.5717 0.4783 0.3512; 

 0.7248 0.7359 0.7429 0.7452 0.7424 0.7335 0.7154... 

 0.6838 0.6366 0.5713 0.4848; 

 0.7427 0.7533 0.7600 0.7627 0.7606 0.7533 0.7379... 

 0.7108 0.6703 0.6147 0.5414; 

 0.7634 0.7736 0.7804 0.7834 0.7822 0.7762 0.7630... 

 0.7394 0.7041 0.6556 0.5920; 

 0.7891 0.8008 0.8090 0.8134 0.8136 0.8092 0.7974... 

 0.7754 0.7417 0.6950 0.6335; 

 0.8139 0.8280 0.8385 0.8449 0.8469 0.8439 0.8333... 

 0.8117 0.7779 0.7303 0.6671; 

 0.8206 0.8356 0.8469 0.8541 0.8567 0.8544 0.8442... 

 0.8229 0.7892 0.7416 0.6783; 

 0.8403 0.8512 0.8593 0.8643 0.8660 0.8641 0.8566... 

 0.8415 0.8179 0.7852 0.7423; 

 0.8408 0.8492 0.8552 0.8588 0.8597 0.8578 0.8516... 

 0.8394 0.8209 0.7954 0.7624; 

 0.8470 0.8505 0.8529 0.8539 0.8536 0.8520 0.8483... 

 0.8418 0.8324 0.8200 0.8043; 

 0.8350 0.8364 0.8371 0.8370 0.8362 0.8346 0.8318... 

 0.8275 0.8217 0.8141 0.8049; 

 0.8202 0.8203 0.8201 0.8195 0.8185 0.8171 0.8152... 

 0.8124 0.8088 0.8045 0.7992]; 

%========== PR = f(NcMap, RlineMap) ================== 

 MWS.HPC.PRArray = [ 2.4769 2.4288 2.3620 2.2778 2.1774 2.0627... 

 1.9284 1.7711 1.5958 1.4083 1.2146; 

 3.4633 3.3778 3.2643 3.1248 2.9619 2.7787... 

 2.5679 2.3253 2.0595 1.7802 1.4973; 

 5.0821 4.9375 4.7554 4.5391 4.2923 4.0194... 

 3.7106 3.3602 2.9800 2.5826 2.1813; 

 6.3490 6.1658 5.9371 5.6667 5.3594 5.0204... 

 4.6377 4.2042 3.7342 3.2431 2.7467; 

 8.0021 7.7686 7.4792 7.1388 6.7532 6.3287... 

 5.8504 5.3097 4.7237 4.1114 3.4919; 

 10.4899 10.1976 9.8249 9.3786 8.8669 8.2989... 

 7.6539 6.9201 6.1229 5.2899 4.4495 ; 

 14.4564 14.0970 13.6074 12.9977 12.2808 11.4715... 

 10.5377 9.4621 8.2878 7.0614 5.8306; 

 17.4426 17.0500 16.4870 15.7661 14.9034 13.9183... 

 12.7692 11.4347 9.9718 8.4425 6.9104; 

 20.7403 20.2486 19.6093 18.8329 17.9324 16.9227... 

 15.7626 14.4263 12.9562 11.3983 9.8011; 

 23.8298 23.2601 22.5536 21.7200 20.7705 19.7178... 

 18.5212 17.1524 15.6466 14.0424 12.3810; 

 26.6962 26.0933 25.4175 24.6733 23.8656 22.9999... 

 22.0495 20.9930 19.8436 18.6163 17.3267; 
NASA/TM—2014-218409 20 

 27.6439 27.0687 26.4522 25.7969 25.1052 24.3798... 

 23.6033 22.7614 21.8600 20.9058 19.9057; 

 28.4663 27.9667 27.4460 26.9054 26.3460 25.7690... 

 25.1640 24.5225 23.8472 23.1399 22.4038]; 

HPT map: 

MWS.HPT.NcVec = [ 60 70 80 90 100 110]; 

 MWS.HPT.PRVec = [ 3.000 3.250 3.500 3.750 4.000 4.250 4.500... 

 4.750 5.000 5.250 5.500 5.750 6.000 6.250... 

 6.500 6.750 7.000 7.250 7.500 8.000]; 

%========== Wc = f(NcMap, PRMap) ================== 

 MWS.HPT.WcArray = [... 

 30.446 30.533 30.568 30.572 30.572 30.572 30.572... 

 30.572 30.572 30.572 30.572 30.572 30.572 30.572... 

 30.572 30.572 30.572 30.572 30.572 30.572 ; 

 30.299 30.413 30.480 30.516 30.529 30.530 30.530... 

 30.530 30.530 30.530 30.530 30.530 30.530 30.530... 

 30.530 30.530 30.530 30.530 30.530 30.530 ; 

 30.120 30.239 30.317 30.368 30.398 30.415 30.421... 

 30.421 30.421 30.421 30.421 30.421 30.421 30.421... 

 30.421 30.421 30.421 30.421 30.421 30.421 ; 

 30.014 30.124 30.201 30.253 30.288 30.311 30.325... 

 30.333 30.337 30.337 30.337 30.337 30.337 30.337... 

 30.337 30.337 30.337 30.337 30.337 30.337 ; 

 29.856 29.948 30.013 30.059 30.091 30.113 30.128... 

 30.139 30.145 30.149 30.150 30.150 30.150 30.150... 

 30.150 30.150 30.150 30.150 30.150 30.150 ; 

 29.799 29.870 29.920 29.955 29.979 29.997 30.009... 

 30.017 30.023 30.026 30.028 30.029 30.029 30.029... 

 30.029 30.029 30.029 30.029 30.029 30.029]; 

 

 

 

%========== eff = f(NcMap, PRMap) ================== 

 MWS.HPT.EffArray = [... 

 0.8460 0.8405 0.8349 0.8296 0.8249 0.8206 0.8165... 

 0.8127 0.8092 0.8060 0.8030 0.8002 0.7976 0.7953... 

 0.7931 0.7911 0.7892 0.7875 0.7858 0.7826 ; 

 0.8879 0.8842 0.8804 0.8769 0.8735 0.8701 0.8670... 

 0.8640 0.8614 0.8590 0.8568 0.8548 0.8529 0.8511... 

 0.8495 0.8479 0.8460 0.8436 0.8414 0.8373 ; 

 0.9125 0.9111 0.9096 0.9078 0.9055 0.9034 0.9014... 

 0.8995 0.8979 0.8964 0.8950 0.8936 0.8924 0.8903... 

 0.8877 0.8853 0.8830 0.8808 0.8787 0.8749 ; 

 0.9228 0.9242 0.9250 0.9247 0.9240 0.9232 0.9224... 

 0.9217 0.9210 0.9203 0.9197 0.9188 0.9162 0.9137... 

 0.9113 0.9091 0.9070 0.9050 0.9031 0.8980 ; 

 0.9215 0.9258 0.9289 0.9304 0.9313 0.9319 0.9323... 

 0.9326 0.9328 0.9329 0.9330 0.9311 0.9288 0.9266... 

 0.9245 0.9225 0.9206 0.9188 0.9161 0.9107 ; 

 0.9106 0.9176 0.9232 0.9267 0.9292 0.9312 0.9327... 

 0.9340 0.9351 0.9361 0.9369 0.9349 0.9329 0.9311... 

 0.9293 0.9276 0.9259 0.9239 0.9212 0.9161]; 
NASA/TM—2014-218409 21 

LPT map: 

MWS.LPT.NcVec = [ 60 70 80 90 100 110 120]; 

 MWS.LPT.PRVec = [ 3.000 3.250 3.500 3.750 4.000 4.250 4.500... 

 4.750 5.000 5.250 5.500 5.750 6.000 6.250... 

 6.500 6.750 7.000 7.250 7.500 8.000]; 

%========== Wc = f(NcMap, PRMap) ================== 

 MWS.LPT.WcArray = [... 

 153.812 153.812 153.812 153.812 153.812 153.812 153.812... 

 153.812 153.812 153.812 153.812 153.812 153.812 153.812... 

 153.812 153.812 153.812 153.812 153.812 153.812 ; 

 153.511 153.511 153.511 153.511 153.511 153.511 153.511... 

 153.511 153.511 153.511 153.511 153.511 153.511 153.511... 

 153.511 153.511 153.511 153.511 153.511 153.511 ; 

 152.799 152.982 153.052 153.061 153.061 153.061 153.061... 

 153.061 153.061 153.061 153.061 153.061 153.061 153.061... 

 153.061 153.061 153.061 153.061 153.061 153.061 ; 

 150.995 151.316 151.518 151.647 151.729 151.781 151.814... 

 151.834 151.846 151.852 151.856 151.858 151.859 151.859... 

 151.859 151.859 151.859 151.859 151.859 151.859 ; 

 148.751 149.107 149.349 149.517 149.635 149.719 149.779... 

 149.822 149.852 149.872 149.885 149.894 149.898 149.899... 

 149.899 149.899 149.899 149.899 149.899 149.899 ; 

 145.352 145.680 145.905 146.061 146.169 146.244 146.293... 

 146.324 146.339 146.344 146.344 146.344 146.344 146.344... 

 146.344 146.344 146.344 146.344 146.344 146.344 ; 

 140.863 141.131 141.310 141.428 141.503 141.547 141.567... 

 141.569 141.569 141.569 141.569 141.569 141.569 141.569... 

 141.569 141.569 141.569 141.569 141.569 141.569]; 

 

 

%========== eff = f(NcMap, PRMap) ================== 

 MWS.LPT.EffArray = [... 

 0.8388 0.8309 0.8234 0.8159 0.8091 0.8030 0.7975... 

 0.7924 0.7876 0.7832 0.7791 0.7753 0.7717 0.7684... 

 0.7652 0.7623 0.7595 0.7568 0.7542 0.7495; 

 0.8878 0.8813 0.8745 0.8685 0.8629 0.8577 0.8528... 

 0.8484 0.8443 0.8404 0.8368 0.8334 0.8302 0.8272... 

 0.8242 0.8210 0.8179 0.8150 0.8122 0.8071; 

 0.9201 0.9152 0.9105 0.9061 0.9018 0.8978 0.8940... 

 0.8905 0.8872 0.8840 0.8810 0.8776 0.8741 0.8707... 

 0.8676 0.8646 0.8618 0.8590 0.8565 0.8516; 

 0.9381 0.9360 0.9336 0.9310 0.9283 0.9257 0.9231... 

 0.9206 0.9182 0.9153 0.9119 0.9087 0.9056 0.9027... 

 0.8999 0.8973 0.8948 0.8924 0.8901 0.8858; 

 0.9447 0.9455 0.9456 0.9450 0.9440 0.9429 0.9417... 

 0.9404 0.9383 0.9355 0.9327 0.9301 0.9276 0.9252... 

 0.9229 0.9207 0.9186 0.9165 0.9146 0.9099; 

 0.9415 0.9454 0.9479 0.9495 0.9504 0.9510 0.9512... 

 0.9511 0.9492 0.9472 0.9452 0.9433 0.9414 0.9396... 

 0.9378 0.9361 0.9344 0.9326 0.9304 0.9262; 

 0.9295 0.9366 0.9419 0.9458 0.9487 0.9509 0.9526... 

 0.9538 0.9528 0.9517 0.9505 0.9493 0.9481 0.9468... 

 0.9456 0.9444 0.9432 0.9413 0.9395 0.9360]; 
NASA/TM—2014-218409 22 

C. T-MATS Parameters 

TABLE 9.—ADDITIONAL REQUIRED T-MATS CONSTANTS 

T-MATS 

component 

NPSS 

variable 

T-MATS variable Value Description Method 

Inlet 

eRam eRambase_M 0.992 Base dP across inlet Per Data 

eRam 

derived X_eRamVec_M 

[0.99 1 1.007 

1.028 1.1 2] Ram dP vector 

Determined empirically by 

viewing change in pressure as 

Pt/Pa is changed 

eRam 

derived T_eRamtbl_M 

[1 1 1.001 

1.002 1.003 

1.003] 

Ram dP pressure 

multiplier 

Determined empirically by 

viewing change in pressure as 

Pt/Pa is changed 

HPC 

Bleeds - 

Wb/Win C_FBD_M [0.55 0.035] 

Fractional bleed 

demand, for each 

bleed Per Data, Bleed - output 

Bleeds - 

ht C_BFht_M [1 1] 

Fractional bleed 

enthalpy 

Calculated by assuming enthalpy 

rises linearly from component 

input to output. 

Bleeds - 

Pt C_BFPt_M [1 1] 

Fraction bleed 

pressure 

Calculated by assuming enthalpy 

rises linearly from component 

input to output. 

Burner 

LHV LHV_M 18400 Lower Heating Value 

Per Data, from model definition 

file 

dPnorm dPnormBurner_M 0.055 dP across Burner Per Data 

eff Eff_M 0.944 Burner Efficiency Per Data 

HPT 

C_HPT 

exit or 

inlt CoolFlwPos_M [0 1] 

Location of input 

cooling flows 

Per Data, HPT_in - 0 , 

HPT_exit - 1 

Core nozzle 

Ath N_Tarea_M 862.88 Nozzle throat area Per Data 

Cv CvArray_M [0.999 0.999] Cv value 

Per Data, in this instance the 

value is constant 

Byp nozzle Ath N_Tarea_M 2706.4 

Bypass nozzle throat 

area Per Data 

Cv CvArray_M 

[0.9975 

0.9975] Cv value 

Per Data, in this instance the 

value is constant 

Duct1 dPnorm dP_M 0.0025 dP loss across duct1 Per Data 

Duct2 dPnorm dP_M 0.0025 dP loss across duct2 Per Data 

Duct3 dPnorm dP_M 0.005 dP loss across duct3 Per Data 

Duct4 dPnorm dP_M 0.01 dP loss across duct4 Per Data 

Duct5 dPnorm dP_M 0.0075 dP loss across duct5 Per Data 

HP shaft 

None Shaft_Inertia_M 20 

High Pressure Shaft 

Inertia 

Assumption based on engine 

class. This is a dynamic criteria 

and NPSS data is steady state. 

LP shaft 

None Shaft_Inertia_M 100 

Low Pressure Shaft 

Inertia 

Assumption based on engine 

class. This is a dynamic criteria 

and NPSS data is steady state. 

 
NASA/TM—2014-218409 23 

References 

1. Jones, S.M., “An Introduction to Thermodynamic Performance Analysis of Aircraft Gas Turbine 

Engine Cycles Using the Numerical Propulsion System Simulation Code,” NASA/TM—2007-

214690, March 2007. 

2. Jones, S.M., “Steady-State Modeling of Gas Turbine Engines Using The Numerical Propulsion 

System Simulation Code,” GT2010-22350, June 2010. 

3. Nichols, L.D. and Chamis, C.C., “Numerical Propulsion System Simulation: An Interdisciplinary 

Approach,” AIAA-91-3554, September 1991. 

4. May, R.D., Csank, J., Lavelle, T.M., Litt, J.S., and Guo T.H., “A High-Fidelity Simulation of a 

Generic Commercial Aircraft Engine and Controller,” NASA/TM—2010-216810, October 2010. 

5. DeCastro, J.A., Litt, J.S., Frederick, D.K., “A Modular Aero-Propulsion System Simulation of a 

Large Commercial Aircraft Engine,” NASA/TM—2008-215303, January 2008. 

6. Chapman, J.W., Lavelle, T.M., May, R.D., Litt, J.S., and Guo, T.M., “Toolbox for the Modeling and 

Analysis of Thermodyanmic Systems (T-MATS) User’s Guide,” NASA/TM—2014-216638, 

January 2014. 

7. Chapman, J.W., Lavelle, T.M., May, R.D., Litt, J.S., Guo, T-H., “Propulsion System Simulation 

Using the Toolbox for the Modeling and Analysis of Thermodynamic Systems (T-MATS),” 2014 

AIAA Joint Propulsion Conference, Cleveland, OH, Jul 28-30, 2014. 

8. Zinnecker, A.M., Chapman, J.W., Lavelle, T.M., and Litt, J.S., “Development of a twin-spool 

turbofan engine simulation using the Toolbox for the Modeling and Analysis of Thermodynamic 

Systems (T-MATS),” 2014 AIAA Joint Propulsion Conference, Cleveland, OH, Jul 28-30, 2014. 

9. Daly, M., Jane’s Aero Engines, Issue 28, Ed., Jane’s Information Group, London, England, 

September 2010. 

10. Lavelle, T.M., Chapman, J.W., May, R.D., Litt, J.S., and Guo, T.H., “Cantera Integration with the 

Toolbox for the Modeling and Analysis of Thermodynamic Systems (T-MATS),” 2014 AIAA Joint 

Propulsion Conference, Cleveland, OH, Jul 28-30, 2014.