Transient Behavior in Variable Geometry Industrial Gas Turbines: A Comprehensive Overview of Pertinent Modeling Techniques
Abstract
:1. Introduction
1.1. Literature Survey of Transient Modeling Domains
1.2. Research Gaps
 To the author’s best knowledge, there is a lack of organized literature review so far that may cover all the possible techniques and methods for the development of transient models of industrial gas turbine regarding fault detection and diagnostics (FDD).
 The pertinent literature for variable geometry features (i.e., VIGVs, VSVs, variable bleed and VAN) that play significant role in engine’s reliability preventing engine from surging during transient behavior, remained shallow.
 There is no such existing document that provides accurate data for shaft’s polar moment of inertia required for accurate transient model development
 To date, there is no authentic document that aids in selection of proper VIGV and bleed schedules for a particular IGT engine based on its inherent configuration, i.e., single shaft, twin shaft, and triple shaft
2. Classifications of Transient Regimes in IGT
2.1. Startup
2.2. Load Change (Acceleration and Deceleration)
2.3. Shutdown
2.4. Secondary Transient Effects
3. Methods and Techniques for Transient Models
3.1. White Box Models
3.2. Black Box Models
3.3. Other Models
4. Transient Model Development Portfolio of IGTs
4.1. Shaft Dynamics
Authors  Polar Moment of Inertia (kgm^{2})  Configuration of Engine  

$\mathbf{GG}\text{}\left({\mathit{J}}_{\mathit{G}\mathit{G}\mathit{S}}\right)$  $\mathbf{PT}\left({\mathit{J}}_{\mathit{P}\mathit{T}\mathit{S}}\right)$  
Gaudet, [145]  0.08  0.05  Twin shaft (Marine) 
Janikovic, [140]  30–50  50  Twin shaft (Turbofan) 
Novikov, [55]  0.060334  1.3694  Twin shaft (Turboshaft) 
Silva, [146]  0.55  0.35  Twin shaft (Turboshaft) 
Barbosa et al. [147]  0.0125    Single shaft (Turbojet) 
Kim et al. [64]  1.14  1.60  Three shaft (Turbofan) 
Kim et al. [72]  0.02    Single shaft (IGT) 
4.2. Volume Dynamics
4.2.1. Constant Mass Flow Method
4.2.2. Inter Component Volume (ICV) Method
4.3. Inlet and Exhaust Duct Modeling
4.4. Compressor Modeling
4.5. Combustor Modeling
4.6. Turbine Modeling Methods
5. Control Strategies for Dynamic Operations
5.1. Simplified PID Control Scheme
5.2. Model Based Control Schemes
5.3. Fuel Flow Actuation
5.4. VIGV Actuation
5.4.1. VIGV Schedule Selection Framework
5.4.2. VIGV Modulation Correction Factors
5.5. Variable Bleed Actuation
6. Software Tools for Transient Modeling
6.1. ZeroDimensional Simulation Programs
6.2. MultiDimensional Simulation Programs
7. Future Recommendations
8. Conclusions
 Although, variety of pertinent transient models exits in the literature, there is a scarcity in transient models for variable geometry IGT.
 Control mechanisms associated with VIGV and VBV are indispensable for different transient regimes, i.e., startup load change and shutdown.
 The VIGV schedule selection framework along with VIGV schedule database play a vital role in academic modeling and real time operation and maintenance of IGT. For instance, framework can be beneficial during maintenance for proper calibration of a drifted VIGV schedule.
 The polar moment of inertia for several configuration of IGTs delineates a paramount importance for accurate modeling of transient behavior in variable geometry IGT
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
Nomenclature  $Max$  Maximum  
$e$  Internal energy per unit mass  $Min$  Minimum 
$F$  Force  $M$  Mean value 
$\mathit{F}$  Force Vector  $to$  total 
$H$  Total enthalpy  $to,in$  total inlet 
$\dot{m}$  mass flow rate  $cc$  combustion chamber 
$\mathit{n}$  unit vector normal to the surface  $DP$  Design Point 
$p$  static pressure  $VIGV$  VIGV corrected value 
$\dot{Q}$  Heat transfer  $FG,map$  Fixed Geometry compressor map 
$S$  Surface  $a,b,c,{c}_{1},{c}_{2},{c}_{3},$ ${K}_{v},{K}_{T},{K}_{m},{K}_{E}$  VIGV correction factors 
$t$  time  $OD$  Off design 
$A$  Area  $Max,\eta $  Maximum efficiency value 
$u$  Axial velocity  $corr$  corrected value 
$\mathit{u}$  velocity vector  $corr,map$  corrected values from maps 
$V$  Volume  $dis$  discharge value 
$\dot{W}$  power  $v,max$  maximum extent of bleed valve opening 
$\omega $  angular velocity  Greek Letters  
$J$  Polar moment of inertia  $\rho $  density 
$N$  shaft rotational speed  ${\tau}_{I}$  Inertial time constant 
$m$  mass  $\mathsf{\Delta}$  Change 
$r$  Engine radius  ${\tau}_{c}$  Compressor Torque 
$P$  Total Pressure  $\eta $  isentropic efficiency 
$T$  Total temperature  $\gamma $  polytropic index 
$R$  Gas Constant  $\varphi $  flow coefficient 
${C}_{p}$  specific heat at constant pressure  $\psi $  pressure coefficient 
$d$  diameters  $\xi $  temperature rise coefficient 
$U$  tangential blade speed  $\alpha $  flow angle relative to a stator 
$P{R}_{s}$  stage pressure ratio  $\beta $  flow angle relative to a rotor 
$G$  Generalized functions  ${\tau}_{cc}$  burner time constant 
$a$  numbers of variables at each control surface  ${\theta}_{VIGV}$  VIGV angle 
$Z=3\left(n+1\right)$  total number of variables  ${\theta}_{VAN}$  VAN angle 
${C}_{D}$  Drag Coefficient  $\overline{\omega}$  Total pressure loss coefficient 
$h$  enthalpy  $\sigma $  Pressure ration between compressor inlet and sea level 
$K$  Stodola Constant  Abbreviations  
$\kappa $  Choking constant  SF  shape factor 
$u\left(t\right)$  input signal  CCPP  combined cycle power plant 
$y\left(t\right)$  Output signal  FDD  fault detection and diagnostics 
$r\left(t\right)$  Demanded signal  GA  Genetic algorithm 
$e\left(t\right)$  Error signal  GG  Gas Generator 
${K}_{p}$  proportional controller gain  HRSG  Heat Recovery steam generator 
${K}_{i}$  integral controller gain  ICV  Intercomponent volume 
${K}_{d}$  derivative controller gain  CMF  Constant Mass Flow 
${C}_{g}$  extent of bleed valve opening  IGT  Industrial gas turbines 
Subscripts  VIGV  Variable inlet guide vane  
$i$  control volume index  VSV  Variable Stator vane 
$in$  inlet  VAN  Variable area nozzle 
$out$  outlet  VBV  variable bleed valve 
$t$  turbine  NGV  Nozzle guide vane 
$c$  compressor  ODEs  Ordinary Differential equations 
$f$  fictional power loss  PDEs  partial differential equations 
$el$  electric load  OOP  Object oriented programming 
$s$  shaft  TIT  Turbine inlet temperature 
$d$  design  TET  Turbine exhaust temperature 
$target,Eng$  Target Engine  HPC  High pressure compressor 
$ref,Eng$  Reference Engine  HPT  High pressure turbine 
$GGS$  gas generator shaft  LPT  Low pressure turbine 
$PTS$  Power turbine shaft  ANN  Artificial neural network 
$1$  transition stage between to control volume  CFD  Computational fluid dynamics 
$a$  air  CMs  continuity models 
$g$  Gas  TFMs  Transfer function models 
$in,d$  intake design point value  LFMs  Linear function models 
$1,2,3,4$  station numbers 
References
 Razak, A. Industrial Gas Turbines: Performance and Operability; Elsevier: Amsterdam, The Netherlands, 2007. [Google Scholar]
 Ahsan, S.; Lemma, T.A. Remaining Useful Life Prediction of Gas Turbine Engine using Autoregressive Model. In Proceedings of the MATEC Web of Conferences, Perak, Malaysia, 25 September 2017; p. 04014. [Google Scholar]
 Ahsan, S.; Lemma, T.A.; Gebremariam, M.A. Reliability analysis of gas turbine engine by means of bathtubshaped failure rate distribution. Process. Saf. Prog. 2020, 39, e12115. [Google Scholar] [CrossRef] [Green Version]
 Boyce, M.P. Gas Turbine Engineering Handbook; Elsevier: Amsterdam, The Netherlands, 2011. [Google Scholar]
 Kurz, R.; Brun, K. Gas Turbine TutorialMaintenance And Operating Practices Effects On Degradation And Life. In Proceedings of the 36th Turbomachinery Symposium, Houston, TX, USA, 11 September 2007. [Google Scholar]
 Thames, J.; Stueber, H.; Vincent, C. Design and Performance Features of the Marine LM1600 Gas Turbine. In Proceedings of the ASME 1990 International Gas Turbine and Aeroengine Congress and Exposition, American Society of Mechanical Engineers, Brussels, Belgium, 11 June 1990; p. V002T003A005. [Google Scholar]
 Shin, J.; Jeon, Y.; Maeng, D.; Kim, J.; Ro, S. Analysis of the dynamic characteristics of a combinedcycle power plant. Energy 2002, 27, 1085–1098. [Google Scholar] [CrossRef]
 Ahsan, S.; Lemma, T.; Muhammad, M. Prognosis of gas turbine remaining useful life using particle filter approach. Materialwissenschaft Werkstofftechnik 2019, 50, 336–345. [Google Scholar] [CrossRef]
 Tsoutsanis, E.; Meskin, N.; Benammar, M.; Khorasani, K. Dynamic performance simulation of an aeroderivative gas turbine using the matlab simulink environment. In Proceedings of the ASME 2013 International Mechanical Engineering Congress and Exposition, American Society of Mechanical Engineers, San Diego, CA, USA, 15 November 2013; p. V04AT04A050. [Google Scholar]
 White, M.F. An Investigation of Component Deterioration in Gas Turbines Using Transient Performance Simulation. In Proceedings of the ASME 1988 International Gas Turbine and Aeroengine Congress and Exposition, American Society of Mechanical Engineers, Amsterdam, The Netherlands, 6 June 1988; p. V005T015A011. [Google Scholar]
 Hashmi, M.B.; Lemma, T.A.; Karim, A.; Ambri, Z. Investigation of the Combined Effect of Variable Inlet Guide Vane Drift, Fouling, and Inlet Air Cooling on Gas Turbine Performance. Entropy 2019, 21, 1186. [Google Scholar] [CrossRef] [Green Version]
 Kim, J.; Song, T.; Kim, T.; Ro, S. Dynamic simulation of full startup procedure of heavy duty gas turbines. In Proceedings of the ASME Turbo Expo 2001: Power for Land, Sea, and Air, American Society of Mechanical Engineers, New Orleans, LA, USA, 4–7 June 2001; p. V004T004A010. [Google Scholar]
 Haglind, F. Variable geometry gas turbines for improving the partload performance of marine combined cycles–Combined cycle performance. Appl. Therm. Eng. 2011, 31, 467–476. [Google Scholar] [CrossRef] [Green Version]
 Bringhenti, C.; Barbosa, J. Methodology for gas turbine performance improvement using variablegeometry compressors and turbines. Proc. Inst. Mech. Eng. Part A J. Power Energy 2004, 218, 541–549. [Google Scholar] [CrossRef]
 Haglind, F. Variable geometry gas turbines for improving the partload performance of marine combined cycles–gas turbine performance. Energy 2010, 35, 562–570. [Google Scholar] [CrossRef]
 Tahan, M.; Tsoutsanis, E.; Muhammad, M.; Karim, Z.A. Performancebased health monitoring, diagnostics and prognostics for conditionbased maintenance of gas turbines: A review. Appl. Energy 2017, 198, 122–144. [Google Scholar] [CrossRef] [Green Version]
 Hung, W. Dynamic simulation of gasturbine generating unit. C Gener. Transm. Distrib. 1991, 138, 342–350. [Google Scholar] [CrossRef]
 Botros, K.; Campbell, P.; Mah, D. Dynamic simulation of compressor station operation including centrifugal compressor and gas turbine. In Proceedings of the ASME 1990 International Gas Turbine and Aeroengine Congress and Exposition, American Society of Mechanical Engineers, Brussels, Belgium, 11 June 1990; p. V003T007A011. [Google Scholar]
 Badmus, O.; Eveker, K.; Nett, C. Controloriented highfrequency turbomachinery modeling: General onedimensional model development. J. Turbomach. 1995, 117. [Google Scholar] [CrossRef]
 Badmus, O.; Eveker, K.; Nett, C. Controloriented highfrequency turbomachinery modeling: General 1D model development. In Proceedings of the ASME 1993 International Gas Turbine and Aeroengine Congress and Exposition, Nashville, TN, USA, 6 June 1992. [Google Scholar]
 Badmus, O.; Eveker, K.; Nett, C. ControlOriented High Frequency Turbomachinery Modeling; American Institute of Aeronautics and Astronautics (AIAA): Nashville, TN, USA, 1992. [Google Scholar]
 Lichtsinder, M.; Levy, Y. Jet engine model for control and realtime simulations. J. Eng. Gas Turbines Power 2006, 128, 745–753. [Google Scholar] [CrossRef]
 Tsoutsanis, E.; Meskin, N. Dynamic performance simulation and control of gas turbines used for hybrid gas/wind energy applications. Appl. Therm. Eng. 2019, 147, 122–142. [Google Scholar] [CrossRef] [Green Version]
 Park, J.c. Modeling and Simulation of Selected Distributed Generation Sources and Their Assessment. Graduate Theses, Dissertations, and Problem Reports. 1999, p. 989. Available online: https://researchrepository.wvu.edu/etd/989 (accessed on 20 October 2020).
 Li, J.; Zhang, G.; Ying, Y.; Shi, W.; Bi, D. Marine ThreeShaft IntercooledCycle Gas Turbine Engine Transient Thermodynamic Simulation. Int. J. Perform. Eng. 2018, 14, 2289–2301. [Google Scholar] [CrossRef] [Green Version]
 Pires, T.S.; Cruz, M.E.; Colaço, M.J.; Alves, M.A. Application of nonlinear multivariable model predictive control to transient operation of a gas turbine and NOX emissions reduction. Energy 2018, 149, 341–353. [Google Scholar] [CrossRef]
 Tsoutsanis, E.; Meskin, N. Performance assessment of classical and fractional controllers for transient operation of gas turbine engines. IFACPapersOnLine 2018, 51, 687–692. [Google Scholar] [CrossRef]
 Bahrami, S.; Ghaffari, A.; Thern, M. Improving the transient performance of the gas turbine by steam injection during frequency dips. Energies 2013, 6, 5283–5296. [Google Scholar] [CrossRef] [Green Version]
 Takahashi, K.; Yasuda, T.; Endoh, M.; Kurosaki, M. Application of dynamic simulation to caes G/T control system development. In Proceedings of the ASME Turbo Expo 2002: Power for Land, Sea, and Air, Amsterdam, The Netherlands, 3 June 2002; pp. 153–161. [Google Scholar]
 Ailer, P.; Sįnta, I.; Szederkényi, G.; Hangos, K.M. Nonlinear modelbuilding of a lowpower gas turbine. Period. Polytech. Transp. Eng. 2001, 29, 117–135. [Google Scholar]
 Badmus, O.; Eveker, K.; Nett, C. Controloriented highfrequency turbomachinery modeling. ITheoretical foundations. In Proceedings of the 28th Joint Propulsion Conference and Exhibit, Nashville, TN, USA, 6 June 1992; p. 3314. [Google Scholar]
 Kong, C.D.; Kim, S. Real Time Linear Simulation and Control for the Small Aircraft Turbojet Engine. In Proceedings of the ASME 1997 Turbo Asia Conference, Singapore, 30 October 1997; p. V001T001A003. [Google Scholar]
 Bettocchi, R.; Spina, P.; Fabbri, F. Dynamic modeling of singleshaft industrial gas turbine. In Proceedings of the ASME 1996 International Gas Turbine and Aeroengine Congress and Exhibition, Birmingham, UK, 10–13 June 1996; p. V004T011A007. [Google Scholar]
 Mehrpanahi, A.; Hamidavi, A.; Ghorbanifar, A. A novel dynamic modeling of an industrial gas turbine using condition monitoring data. Appl. Therm. Eng. 2018, 143, 507–520. [Google Scholar] [CrossRef]
 Mehrpanahi, A.; Payganeh, G.; Arbabtafti, M. Dynamic modeling of an industrial gas turbine in loading and unloading conditions using a gray box method. Energy 2017, 120, 1012–1024. [Google Scholar] [CrossRef]
 Sekhon, R.; Bassily, H.; Wagner, J.; Gaddis, J. Stationary gas turbinesa real time dynamic model with experimental validation. In Proceedings of the American Control Conference, Minneapolis, MN, USA, 14–16 June 2006; p. 7. [Google Scholar]
 Giuntini, S.; Andreini, A.; Facchini, B.; Mantero, M.; Pirotta, M.; Olmes, S.; Zierer, T. Transient thermal modelling of whole gt engine with a partly coupled femfluid network approach. In Proceedings of the ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition, Charlotte, NC, USA, 26–30 June 2017; p. V05BT15A026. [Google Scholar]
 Tsoutsanis, E.; Meskin, N.; Benammar, M.; Khorasani, K. Transient gas turbine performance diagnostics through nonlinear adaptation of compressor and turbine maps. J. Eng. Gas Turbines Power 2015, 137, 091201. [Google Scholar] [CrossRef]
 MeherHomji, C.B.; Bhargava, R. Condition monitoring and diagnostic aspects of gas turbine transient response. In Proceedings of the ASME 1992 International Gas Turbine and Aeroengine Congress and Exposition, Cologne, Germany, 1–4 June 1992; p. V004T011A006. [Google Scholar]
 Liu, Z.; Karimi, I. Simulation and optimization of a combined cycle gas turbine power plant for partload operation. Chem. Eng. Res. Des. 2018, 131, 29–40. [Google Scholar] [CrossRef]
 Solomon, A. Dynamic Modeling of Airborne Gas Turbine Engines. In Topics in Control and Its Applications; Springer: Berlin/Heidelberg, Germany, 1999; pp. 189–205. [Google Scholar]
 Ma, S.; Tan, J.; Ning, Y.; Gao, Z. Modeling and simulation of gas turbine starter and fuel control system. In Proceedings of the 2017 36th Chinese Control Conference (CCC), Dalian, China, 26 July 2017; pp. 2149–2154. [Google Scholar]
 Wang, C.; Li, Y.G.; Yang, B.Y. Transient performance simulation of aircraft engine integrated with fuel and control systems. Appl. Therm. Eng. 2017, 114, 1029–1037. [Google Scholar] [CrossRef] [Green Version]
 Singh, V.; Axelsson, L.U.; Visser, W. Transient Performance Analysis of an Industrial Gas Turbine Operating on LowCalorific Fuels. J. Eng. Gas Turbines Power 2017, 139, 051401. [Google Scholar] [CrossRef]
 Kim, J.H.; Kim, T.S.; Moon, S.J. Development of a program for transient behavior simulation of heavyduty gas turbines. J. Mech. Sci. Technol. 2016, 30, 5817–5828. [Google Scholar] [CrossRef]
 Metzger, A. Dynamic Simulation of the FT82™ Gas Turbine. In Proceedings of the ASME 1995 International Gas Turbine and Aeroengine Congress and Exposition, Houston, TX, USA, 5 June 1995; p. V005T015A011. [Google Scholar]
 Rosfjord, T.J.; Cohen, J.M. Evaluation of the transient operation of advanced gas turbine combustors. J. Propuls. Power 1995, 11, 497–504. [Google Scholar] [CrossRef]
 Badami, M.; Ferrero, M.G.; Portoraro, A. Dynamic parsimonious model and experimental validation of a gas microturbine at partload conditions. Appl. Therm. Eng. 2015, 75, 14–23. [Google Scholar] [CrossRef]
 Kyprianidis, K.; Kalfas, A.I. Dynamic performance investigations of a turbojet engine using a crossapplication visual oriented platform. Aeronaut. J. 2008, 112, 161–169. [Google Scholar] [CrossRef]
 Kong, C.; Roh, H.; Lim, K. SteadyState and Transient Simulation of Turbodrop Engine Using SIMULINK® Model. In Proceedings of the ASME Turbo Expo 2003, collocated with the 2003 International Joint Power Generation Conference, Atlanta, GA, USA, 16 June 2003; pp. 151–161. [Google Scholar]
 Kim, S.K.; Pilidis, P.; Yin, J. Gas turbine dynamic simulation using Simulink®; 01487191; SAE Technical Paper: 2000. In Proceedings of the SAE Power Systems Conference 2000P359, San Diego, CA, USA, 31 October 2000. [Google Scholar] [CrossRef]
 Ganji, A.; Khadem, M.; Khandani, S. Transient dynamics of gas turbine engines. In Proceedings of the ASME 1993 International Gas Turbine and Aeroengine Congress and Exposition, Cincinnati, OH, USA, 24 May 1993; p. V03CT17A014. [Google Scholar]
 Lichtsinder, M.; Levy, Y. Evaluation of an Effective Engine Nozzle Map by Reduction of Data Acquired During Transient Operation. In Proceedings of the ASME Turbo Expo 2004: Power for Land, Sea, and Air, Vienna, Austria, 14 June 2004; pp. 55–63. [Google Scholar]
 Shi, Y.; Tu, Q.; Jiang, P.; Zheng, H.; Cai, Y. Investigation of the Compressibility Effects on Engine Transient Performance. In Proceedings of the ASME Turbo Expo 2015: Turbine Technical Conference and Exposition, Montreal, QC, Canada, 15 June 2015; p. V001T001A017. [Google Scholar]
 Novikov, Y. Development of a HighFidelity Transient Aerothermal Model for a Helicopter Turboshaft Engine for Inlet Distortion and Engine Deterioration Simulations. Middle East Tech. Univ. Turk. 2012. Available online: https://hdl.handle.net/11511/21585 (accessed on 20 October 2020).
 Mohammadian, P.K.; Saidi, M.H. Simulation of startup operation of an industrial twinshaft gas turbine based on geometry and control logic. Energy 2019, 183, 1295–1313. [Google Scholar] [CrossRef]
 MontazeriGh, M.; Fashandi, S.A.M.; Abyaneh, S. Realtime simulation testbed for an industrial gas turbine engine’s controller. Mech. Ind. 2018, 19, 311. [Google Scholar] [CrossRef]
 Schobeiri, M.T. Impact of Turbine Blade Stagger Angle Adjustment on the Efficiency and Performance of Gas Turbines During OffDesign and Dynamic Operation. In Proceedings of the ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition, Lillestrøm (Oslo), Norway, 11 June 2018. [Google Scholar]
 Wang, T.; Tian, Y.S.; Yin, Z.; Gao, Q.; Tan, C.Q. Triaxial Gas Turbine Performance Analysis for Variable Power Turbine Inlet Guide Vane Control Law Optimization. In Proceedings of the ASME 2018 International Mechanical Engineering Congress and Exposition, Pittsburgh, PA, USA, 9 November 2018. [Google Scholar]
 Silva, V.T.; Bringhenti, C.; Tomita, J.T.; Petit, O. Influence of Variable Geometry Compressor on Transient Performance of CounterRotating Open Rotor Engines. J. Eng. Gas Turbines Power 2018, 140, 121002. [Google Scholar] [CrossRef]
 Wang, T.; Tian, Y.S.; Yin, Z.; Zhang, D.Y.; Ma, M.Z.; Gao, Q.; Tan, C.Q. RealTime Variable Geometry Triaxial Gas Turbine Model for HardwareintheLoop Simulation Experiments. J. Eng. Gas Turbines Power 2018, 140, 092603. [Google Scholar] [CrossRef]
 Enalou, H.B.; Soreshjani, E.A.; Rashed, M.; Yeoh, S.S.; Bozhko, S. A detailed modular governorturbine model for multiplespool gas turbine with scrutiny of bleeding effect. J. Eng. Gas Turbines Power 2017, 139, 114501. [Google Scholar] [CrossRef]
 MontazeriGh, M.; Fashandi, S.A.M. Application of Bond Graph approach in dynamic modelling of industrial gas turbine. Mech. Ind. 2017, 18, 410. [Google Scholar] [CrossRef]
 Kim, S.; Son, C.; Kim, K.; Kim, M.; Min, S. A Numerical Study on Transient Performance Behavior of a Turbofan Engine with Variable Inlet Guide Vane and Bleed Air Schedules. J. Korean Soc. Propuls. Eng. 2015, 19, 52–61. [Google Scholar] [CrossRef]
 Barbosa, J.R.; Bringhenti, C.; Tomita, J.T. Gas turbine transients with controlled variable geometry. In Proceedings of the ASME Turbo Expo 2012: Turbine Technical Conference and Exposition, Copenhagen, Denmark, 11–15 June 2012; pp. 415–421. [Google Scholar]
 Chacartegui, R.; Sánchez, D.; Muñoz, A.; Sánchez, T. Real time simulation of medium size gas turbines. Energy Convers. Manag. 2011, 52, 713–724. [Google Scholar] [CrossRef]
 Barbosa, J.o.R.; dos Santos Silva, F.J.; Tomita, J.T.; Bringhenti, C. Influence of Variable Geometry Transients on the Gas Turbine Performance. In Proceedings of the ASME 2011 Turbo Expo: Turbine Technical Conference and Exposition, Vancouver, BC, Canada, 6 June 2011; pp. 273–281. [Google Scholar]
 Panov, V. Gasturbolib: Simulink library for gas turbine engine modelling. In Proceedings of the ASME Turbo Expo 2009: Power for Land, Sea, and Air, Orlando, FL, USA, 8 June 2009; pp. 555–565. [Google Scholar]
 Silva, F.J.d.S.; Tomita, J.T.; Barbosa, J. Gas Turbines Transient Performance Study For Axial Compressor Operation Characteristics. In Proceedings of the 19th International Congress of Mechanical Engineering, COBEM, Brasilia—DF, Brazil, 5–8 November 2007. [Google Scholar]
 Bringhenti, C.; Tomita, J.T.; de Sousa Júnior, F.; Barbosa, J.R. Gas Turbine Performance Simulation Using an Optimized Axial Flow Compressor. In Proceedings of the ASME Turbo Expo 2006: Power for Land, Sea, and Air, Barcelona, Spain, 8 May 2006. [Google Scholar]
 Camporeale, S.; Fortunato, B.; Mastrovito, M. A modular code for real time dynamic simulation of gas turbines in simulink. J. Eng. Gas Turbines Power 2006, 128, 506–517. [Google Scholar] [CrossRef]
 Kim, J.; Kim, T.; Ro, S. Analysis of the dynamic behaviour of regenerative gas turbines. Proc. Inst. Mech. Eng. Part A J. Power Energy 2001, 215, 339–346. [Google Scholar] [CrossRef]
 Kim, J.; Song, T.; Kim, T.; Ro, S. Model development and simulation of transient behavior of heavy duty gas turbines. J. Eng. Gas Turbines Power 2001, 123, 589–594. [Google Scholar] [CrossRef]
 Kim, S.Y.; Soudarev, B. Transient analysis of a simple cycle gas turbine engine. KSAS Int. J. 2000, 1, 22–29. [Google Scholar]
 PerezBlanco, H.; Henricks, T.B. A gas turbine dynamic model for simulation and control. In Proceedings of the ASME 1998 International Gas Turbine and Aeroengine Congress and Exhibition, Stockholm, Sweden, 2 June 1998. [Google Scholar]
 Boumedmed, A. The Use of Variable Engine Geometry to Improve the Transient Performance of a TwoSpool Turbofan Engine. Ph.D. Thesis, University of Glasgow, Glasgow, Scotland, 1997. [Google Scholar]
 Peretto, A.; Spina, P.R. Comparison of Industrial Gas Turbine Transient Responses Performed by Different Dynamic Models. In Proceedings of the ASME 1997 International Gas Turbine and Aeroengine Congress and Exhibition, Orlando, FL, USA, 2 June 1997. [Google Scholar]
 Nava, P.; Quercioli, V.; Mammoli, T. Dynamic Model of a Two Shaft HeavyDuty Gas Turbine with Variable Geometry. In Proceedings of the ASME 1995 International Gas Turbine and Aeroengine Congress and Exposition, Houston, TX, USA, 5 June 1995. [Google Scholar]
 Ashley, T.; Johnson, D.; Miller, R.; Salem, V. SPEEDTRONIC™ MARK V Gas Turbine Control System; GE Raport, GER3658D; GE Company, 1996. [Google Scholar]
 Walsh, P.P.; Fletcher, P. Gas Turbine Performance; John Wiley & Sons: Hoboken, NJ, USA, 2004. [Google Scholar]
 Benser, W.A. Compressor operation with one or more blade rows stalled. NASA Spec. Publ. 1965, 36, 341. [Google Scholar]
 Kim, J.H.; Kim, T.S. Development of a program to simulate the dynamic behavior of heavyduty gas turbines during the entire startup operation including very early part. J. Mech. Sci. Technol. 2019, 33, 4495–4510. [Google Scholar] [CrossRef]
 Chappell, M.; McLaughlin, P. Approach of modeling continuous turbine engine operation from startup to shutdown. J. Propuls. Power 1993, 9, 466–471. [Google Scholar] [CrossRef]
 Zeng, D.; Zhou, D.; Tan, C.; Jiang, B. Research on ModelBased Fault Diagnosis for a Gas Turbine Based on Transient Performance. Appl. Sci. 2018, 8, 148. [Google Scholar] [CrossRef] [Green Version]
 Ghaffari, A.; Akhgari, R.; Abbasi, E. Modeling and Simulation of MGT70 Gas Turbine StartUp Procedure. Amirkabir J. Mech. Eng. 2017, 49, 129–132. [Google Scholar]
 Gaudet, S.R.; Gauthier, J.D. A simple subidle component map extrapolation method. In Proceedings of the ASME Turbo Expo 2007: Power for Land, Sea, and Air, Montreal, QC, Canada, 14 May 2007. [Google Scholar]
 Sheng, H.; Zhang, T.; Jiang, W. FullRange Mathematical Modeling of Turboshaft Engine in Aerospace. Int. J. Turbo Jet Engines 2016, 33, 309–317. [Google Scholar] [CrossRef]
 Kim, S.; Ellis, S.; Challener, M. Realtime engine modelling of a three shafts turbofan engine: From subidle to Max power rate. In Proceedings of the ASME Turbo Expo 2006: Power for Land, Sea, and Air, Barcelona, Spain, 8 May 2006. [Google Scholar]
 Ki, J.; Kong, C.; Kho, S.; Lee, C. Steadystate and transient performance modeling of smart UAV propulsion system using Simulink. J. Eng. Gas Turbines Power 2009, 131, 031702. [Google Scholar] [CrossRef]
 Kim, J.; Kim, T.; Sohn, J.; Ro, S. Comparative analysis of offdesign performance characteristics of single and two shaft industrial gas turbines. In Proceedings of the ASME Turbo Expo 2002: Power for Land, Sea, and Air, Amsterdam, The Netherlands, 3 June 2002. [Google Scholar]
 Rowen, W.I. Simplified mathematical representations of single shaft gas turbines in mechanical drive service. In Proceedings of the ASME 1992 International Gas Turbine and Aeroengine Congress and Exposition, Cologne, Germany, 1 June 1992. [Google Scholar]
 Lyantsev, O.; Kazantsev, A.; Abdulnagimov, A. Identification method for nonlinear dynamic models of gas turbine engines on acceleration mode. Procedia Eng. 2017, 176, 409–415. [Google Scholar] [CrossRef]
 Yamane, H. High fidelity simulation of turbofan engine acceleration characteristics with effect of combustor performance variation under transient conditions. In Proceedings of the 30th Joint Propulsion Conference and Exhibit, Indianapolis, IN, USA, 27 June 1994; p. 2957. [Google Scholar]
 Poursaeidi, E.; Bazvandi, H. Effects of emergency and fired shut down on transient thermal fatigue life of a gas turbine casing. Appl. Therm. Eng. 2016, 100, 453–461. [Google Scholar] [CrossRef]
 Reddy, V.V.; Selvam, K.; De Prosperis, R. Gas turbine shutdown thermal analysis and results compared with experimental data. In Proceedings of the ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition, Seoul, Korea, 13 June 2016. [Google Scholar]
 Svensdotter, S.; Skelton, L.; Ingle, J. Shutdown Modelling to Extend Operation to Extreme Ambient Conditions. In Proceedings of the ASME Turbo Expo 2007: Power for Land, Sea, and Air, Montreal, QC, Canada, 14 May 2007. [Google Scholar]
 Blotenberg, W. A model for the dynamic simulation of a twoshaft industrial gas turbine with dry low NOx combustor. In Proceedings of the ASME 1993 International Gas Turbine and Aeroengine Congress and Exposition, Cincinnati, OH, USA, 24 May 1993. [Google Scholar]
 Benato, A.; Pierobon, L.; Haglind, F.; Stoppato, A. Dynamic performance of a combined gas turbine and air bottoming cycle plant for offshore applications. In Proceedings of the ASME 2014 12th Biennial Conference on Engineering Systems Design and Analysis, Citeseer, Copenhagen, Denmark, 25 June 2014; p. V002T009A003. [Google Scholar]
 Khalid, S.; Hearne, R. Enhancing dynamic model fidelity for improved prediction of turbofanengine transient performance. In Proceedings of the 16th Joint Propulsion Conference, Hartford, CT, USA, 30 June 1980; p. 1083. [Google Scholar]
 Maccallum, N.; Pilidis, P. The prediction of surge margins during gas turbine transients. In Proceedings of the ASME 1985 International Gas Turbine Conference and Exhibit, Houston, TX, USA, 18 March 1985. [Google Scholar]
 Khalid, S. Role of dynamic simulation in fighter engine design and development. J. Propuls. Power 1992, 8, 219–226. [Google Scholar] [CrossRef]
 Pilidis, P.; Maccallum, N. The effect of heat transfer on gas turbine transients. In Proceedings of the ASME Turbo Expo: Power for Land, Sea, and Air, Dusseldorf, West Germany, 8 June 1986; Volume 79283, p. V001T01A114. [Google Scholar]
 Pilidis, P.; Maccallum, N. A study of the prediction of tip and seal clearances and their effects in gas turbine transients. In Proceedings of the ASME 1984 International Gas Turbine Conference and Exhibit, Amsterdam, The Netherlands, 4 June 1984; p. V001T001A074. [Google Scholar]
 MacCallum, N.; Pilidis, P. Gas turbine transient fuel scheduling with compensation for thermal effects. In Proceedings of the ASME 1986 International Gas Turbine Conference and Exhibit, Dusseldorf, West Germany, 8 June 1986. [Google Scholar]
 Larjola, J. Simulation of Surge Margin Changes due to Heat Transfer Effects in Gas Turbine Transients. In Proceedings of the ASME 1984 International Gas Turbine Conference and Exhibit, Amsterdam, The Netherlands, 4 June 1984; p. V002T004A003. [Google Scholar]
 Nielsen, A.E.; Moll, C.W.; Staudacher, S. Modeling and validation of the thermal effects on gas turbine transients. In Proceedings of the ASME Turbo Expo 2004: Power for Land, Sea, and Air, Vienna, Austria, 14 June 2004; pp. 363–374. [Google Scholar]
 Merkler, R.; Staudacher, S.; Schölch, M.; Schulte, H.; Schmidt, K.J. Simulation of clearance changes and mechanical stresses in transient gas turbine operation by a matrix method. In Proceedings of the 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Tucson, AZ, USA, 10 July 2005; p. 4022. [Google Scholar]
 Merkler, R.S.; Staudacher, S. Modeling of Heat Transfer and Clearance Changes in Transient Performance Calculations: A Comparison. In Proceedings of the ASME Turbo Expo 2006: Power for Land, Sea, and Air, Barcelona, Spain, 8 May 2006; pp. 37–45. [Google Scholar]
 Vieweg, M.; Wolters, F.; Becker, R.G. Comparison of a Heat Soakage Model With Turbofan Transient Engine Data. In Proceedings of the ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition, Charlotte, NC, USA, 26 June 2017. [Google Scholar]
 da Cunha Alves, M.A.; Barbosa, J.R. A step further in gas turbine dynamic simulation. Proc. Inst. Mech. Eng. Part A J. Power Energy 2003, 217, 583–592. [Google Scholar] [CrossRef]
 Schobeiri, M.; Attia, M.; Lippke, C. Nonlinear dynamic simulation of singleand multispool core engines. IComputational method. IISimulation, code validation. J. Propuls. Power 1994, 10, 855–862. [Google Scholar] [CrossRef]
 Uzol, O.; Yavrucuk, I. Simulation of the Transient Response of a Helicopter Turboshaft Engine to hotgas Ingestion. In Proceedings of the ASME Turbo Expo 2008: Power for Land, Sea, and Air, Berlin, Germany, 9 June 2008; pp. 257–262. [Google Scholar]
 Camporeale, S.M.; Fortunato, B.; Dumas, A. Dynamic modelling of recuperative gas turbines. Proc. Inst. Mech. Eng. Part A J. Power Energy 2000, 214, 213–225. [Google Scholar] [CrossRef]
 Saravanamuttoo, H.I.; Rogers, G.F.C.; Cohen, H. Gas Turbine Theory; Pearson Education: London, UK, 2001. [Google Scholar]
 Klotz, R. Investigation of the Dynamic Response of a SingleAxle SingleLoop Jet Engine. Automatisierungstech 1986, 34, 436–445. [Google Scholar] [CrossRef]
 Fawke, A.; Saravanamuttoo, H. Digital computer methods for prediction of gas turbine dynamic response. SAE Trans. 1971, 80, 1805–1813. [Google Scholar]
 Mody, B. Digital Simulation of Gas Turbine SteadyState and Transient Performance for Current and Advanced Marine Propulsion Systems. Thesis; Cranfield University, 2009. Available online: http://hdl.handle.net/1826/3800 (accessed on 20 October 2020).
 Yepifanov, S.; Zelenskyi, R.; Sirenko, F.; Loboda, I. Simulation of Pneumatic Volumes for a Gas Turbine Transient State Analysis. In Proceedings of the ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition, Charlotte, NC, USA, 26 June 2017; p. V006T005A037. [Google Scholar]
 Merrington, G.; Kwon, O.K.; Goodwin, G.; Carlsson, B. Fault detection and diagnosis in gas turbines. In Proceedings of the ASME 1990 International Gas Turbine and Aeroengine Congress and Exposition, Brussels, Belgium, 11 June 1990; p. V005T015A010. [Google Scholar]
 Garrard, G.D. ATEC: The Aerodyanmic Turbine Engine Code for the Analysis of Transient and Dynamic Gas Turbine Engine System Operations. Ph.D. Dissertation, University of Tennessee, Knoxville, TN, USA, 1995. [Google Scholar]
 Daneshvar, K.; Behbahaninia, A.; Khazraii, Y.; Ghaedi, A. Transient Modeling of SinglePressure Combined CyclePower Plant Exposed to Load Reduction. Int. J. Model. Optim. 2012, 2, 64. [Google Scholar] [CrossRef] [Green Version]
 Schobeiri, T. A General Computational Method for Simulation and Prediction of Transient Behavior of Gas Turbines. In Proceedings of the ASME 1986 International Gas Turbine Conference and Exhibit, Dusseldorf, West Germany, 8 June 1986; p. V001T001A070. [Google Scholar]
 Bloem, J.; Van Doorn, M.; Duivestein, S.; Excoffier, D.; Maas, R.; Van Ommeren, E. The fourth industrial revolution. Things Tighten 2014, 8. [Google Scholar]
 Asgari, H.; Venturini, M.; Chen, X.; Sainudiin, R. Modeling and simulation of the transient behavior of an industrial power plant gas turbine. J. Eng. Gas Turbines Power 2014, 136, 061601. [Google Scholar] [CrossRef]
 Asgari, H.; Chen, X.; Sainudiin, R.; Morini, M.; Pinelli, M.; Spina, P.R.; Venturini, M. Modeling and simulation of the startup operation of a heavyduty gas turbine by using NARX models. In Proceedings of the ASME Turbo Expo 2014: Turbine Technical Conference and Exposition, Volume 3A: Coal, Biomass and Alternative Fuels, Cycle Innovations, Electric Power, Industrial and Cogeneration, Düsseldorf, Germany, 16 June 2014; p. V03AT21A003. [Google Scholar]
 Mehrpanahi, A.; Payganeh, G.; Arbabtafti, M.; Hamidavi, A. SemiSimplified BlackBox Dynamic Modeling of an Industrial Gas Turbine Based on Real Performance Characteristics. J. Eng. Gas Turbines Power 2017, 139, 121601. [Google Scholar] [CrossRef]
 Göing, J.; Kellersmann, A.; Bode, C.; Friedrichs, J. System Dynamics of a SingleShaft Turbojet Engine Using Pseudo Bond Graph. In Proceedings of the Symposium der Deutsche Gesellschaft für Luftund Raumfahrt, Darmstadt, Germany, 6 November 2018; pp. 427–436. [Google Scholar]
 MontazeriGh, M.; Miran Fashandi, S.A. Modeling and simulation of a twoshaft gas turbine propulsion system containing a frictional plate–type clutch. Proc. Inst. Mech. Eng. Part M J. Eng. Marit. Environ. 2019, 233, 502–514. [Google Scholar] [CrossRef]
 MontazeriGh, M.; Fashandi, S.A.M. Bond graph modeling of a jet engine with electric starter. Proc. Inst. Mech. Eng. Part G J. Aerosp. Eng. 2019, 233, 3193–3210. [Google Scholar] [CrossRef]
 Varadharajan, R.; Vasa, N.J.; Srinivasa, Y. Reduced order statespace modelling of a twoshaft turbofan engine for control and offdesign performance analysis. Int. J. Autom. Control. 2009, 4, 26–41. [Google Scholar] [CrossRef]
 YC, S.; Lee, B.; Lee, J.; Kim, Y.; Lee, H. A New Methodology for Advanced Gas Turbine Engine Simulation. In Proceedings of the Korean Society of Propulsion Engineers Conference, The Korean Society of Propulsion Engineers, Seoul, Korea, 3–6 March 2004; pp. 369–375. [Google Scholar]
 Martin, S.; Wallace, I.; Bates, D.G. Development and validation of a civil aircraft engine simulation model for advanced controller design. J. Eng. Gas Turbines Power 2008, 130, 051601. [Google Scholar] [CrossRef] [Green Version]
 Marsilio, R. A computational method for gas turbine engines. In Proceedings of the 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NE, USA, 10 January 2005; p. 1009. [Google Scholar]
 Kulikov, G.G.; Thompson, H.A. Dynamic Modelling of Gas Turbines: Identification, Simulation, Condition Monitoring and Optimal Control; Springer Science & Business Media: London, UK, 2013. [Google Scholar]
 BAKER, J. The dynamic simulation of turbine engine compressors. In Proceedings of the 5th Propulsion Joint Specialist, Colorado Springs, CO, USA, 9 June 1969; p. 486. [Google Scholar]
 Ahlbeck, D.R. Simulating a jet gas turbine with an analog computer. Simulation 1966, 7, 149–155. [Google Scholar] [CrossRef]
 Muir, D.E.; Saravanamuttoo, H.I.; Marshall, D. Health monitoring of variable geometry gas turbines for the Canadian Navy. J. Eng. Gas Turbines Power 1989, 111, 244–250. [Google Scholar] [CrossRef]
 Schobeiri, M.; Attia, M.; Lippke, C. GETRAN: A generic, modularly structured computer code for simulation of dynamic behavior of aeroand power generation gas turbine engines. J. Eng. Gas Turbines Power 1994, 116, 483–494. [Google Scholar] [CrossRef]
 Crosa, G.; Pittaluga, F.; Martinengo, A.T.; Beltrami, F.; Torelli, A.; Traverso, F. Heavyduty gas turbine plant aerothermodynamic simulation using simulink. In Proceedings of the ASME 1996 Turbo Asia Conference, Jakarta, Indonesia, 5 November 1996; p. V001T003A004. [Google Scholar]
 Janikovic, J. Gas Turbine Transient Performance Modeling for Engine Flight Path Cycle Analysis. Dissertation, Cranfield University, UK, 2010. Available online: http://dspace.lib.cranfield.ac.uk/handle/1826/7894 (accessed on 20 October 2020).
 Filinov, E.; Kolmakova, D.; Avdeev, S.; Krasilnikov, S. Correlationregression models for calculating the weight of smallscale aircraft gas turbine engines. In Proceedings of the MATEC Web of Conferences, 2018 The 2nd International Conference on Mechanical, System and Control Engineering, EDP Sciences, Moscow, Russia, 21 June 2018; Volume 220, p. 03004. [Google Scholar]
 Kuz’michev, V.; Krupenich, I.; Filinov, E.; Ostapyuk, Y. Comparative Analysis of Mathematical Models for Turbofan Engine Weight Estimation. In Proceedings of the MATEC Web of Conferences, 2018 The 2nd International Conference on Mechanical, System and Control Engineering, EDP Sciences, Moscow, Russia, 21 June 2018; Volume 220, p. 03012. [Google Scholar]
 Tiemstra, J. On the Conceptual Engine Design and Sizing Tool. Thesis, TU Delft, The Netherlands, 2017. Available online: http://resolver.tudelft.nl/uuid:0956782556cf4a9d8898deb5999e23a6 (accessed on 20 October 2020).
 Lolis, P. Development of a Preliminary Weight Estimation Method for Advanced Turbofan Engines. Thesis, Cranfield University, UK, 2014. Available online: http://dspace.lib.cranfield.ac.uk/handle/1826/9244 (accessed on 20 October 2020).
 Gaudet, S.R. Development of a Dynamic Modeling and Control System Design Methodology for Gas Turbines. Master‘s Thesis, Carleton University, Ottawa, ON, Canada, 2008. Available online: https://curve.carleton.ca/7dbb2d9a127d4d938a18eff100099360 (accessed on 20 October 2020).
 dos Santos Silva, F.J. ESTUDO DE DESEMPENHO DE TURBINAS AGAS SOB A INFLUˆENCIA DE TRANSITORIOS DA GEOMETRIA VARIAVEL. Thesis, Instituto Tecnológico de Aeronáutica, São José dos Campos, Brazil, 2011. Available online: https://mecanica.unifesspa.edu.br/images/FrancoJefferds/TD015_2011.pdf (accessed on 20 October 2020).
 Barbosa, J.R.; Bringhenti, C.; Tomita, J.T. A Step Further on the Control of Acceleration of Gas Turbines With Controlled Variable Geometry and Combustion Emissions. In Proceedings of the ASME Turbo Expo 2014: Turbine Technical Conference and Exposition, Düsseldorf, Germany, 16 June 2014; Volume 45653, p. V03AT07A022. [Google Scholar]
 Kurosaki, M.; Sasamoto, M.; Asaka, K.; Nakamura, K.; Kakiuchi, D. An Efficient Transient Simulation Method for a Volume Dynamics Model. In Proceedings of the ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition, GT201875353, V006T05A008, Oslo, Norway, 11 June 2018. [Google Scholar]
 Gilani, S.I.u.H.; Baheta, A.T.; Majid, A.; Amin, M. Thermodynamics approach to determine a gas turbine components design data and scaling method for performance map generation. In Proceedings of the 1st International Conference on Plant Equipment and Reliability (ICPER), Selangor, Malaysia, 27 March 2008. [Google Scholar]
 AlHamdan, Q.Z.; Ebaid, M.S. Modeling and simulation of a gas turbine engine for power generation. J. Eng. Gas Turbines Power 2006, 128, 302–311. [Google Scholar] [CrossRef]
 Zhu, P.; Saravanamuttoo, H. Simulation of an advanced twinspool industrial gas turbine. In Proceedings of the ASME 1991 International Gas Turbine and Aeroengine Congress and Exposition, Orlando, FL, USA, 3 June 1991; p. V003T007A001. [Google Scholar]
 Leylek, Z.; Anderson, W.S.; Rowlinson, G.; Smith, N. An investigation into performance modeling of a small gas turbine engine. In Proceedings of the ASME Turbo Expo 2013: Turbine Technical Conference and Exposition, San Antonio, TX, USA, 3 June 2013; p. V05AT23A007. [Google Scholar]
 Tamiru, A.L.; Hashim, F.; Rangkuti, C. Generating gas turbine component maps relying on partially known overall system characteristics. J. Appl. Sci. 2011, 11, 1885–1894. [Google Scholar] [CrossRef] [Green Version]
 Song, T.; Kim, T.; Kim, J.; Ro, S. Performance prediction of axial flow compressors using stage characteristics and simultaneous calculation of interstage parameters. Proc. Inst. Mech. Eng. Part A J. Power Energy 2001, 215, 89–98. [Google Scholar] [CrossRef]
 Spina, P.R. Gas Turbine performance prediction by using generalized performance curves of compressor and turbine stages. In Proceedings of the ASME Turbo Expo 2002: Power for Land, Sea, and Air, Amsterdam, The Netherlands, 3 June 2002; pp. 1073–1082. [Google Scholar]
 Rodríguez, C.; Sánchez, D.; Chacartegui, R.; Munoz, A.; Martínez, G. Compressor fouling: A comparison of different fault distributions using a “stagestacking” technique. In Proceedings of the ASME Turbo Expo 2013: Turbine Technical Conference and Exposition, San Antonio, TX, USA, 3 June 2013; p. V002T007A001. [Google Scholar]
 Johnson, M.S. Onedimensional, stagebystage, axial compressor performance model. In Proceedings of the ASME 1991 International Gas Turbine and Aeroengine Congress and Exposition, Orlando, FL, USA, 3 June 1991; p. V001T001A070. [Google Scholar]
 Glassman, A.J. Design Geometry and Design/offDesign Performance Computer Codes for Compressors and Turbines; Report; The University of Toledo: Toledo, OH, USA, 1995. [Google Scholar]
 Tahan, M.; Muhammad, M.; Karim, Z.A. Performance evaluation of a twinshaft gas turbine engine in mechanical drive service. J. Mech. Sci. Technol. 2017, 31, 937–948. [Google Scholar] [CrossRef]
 Pierobon, L.; Iyengar, K.; Breuhaus, P.; Kandepu, R.; Haglind, F.; Hana, M. Dynamic performance of power generation systems for offshore oil and gas platforms. In Proceedings of the ASME Turbo Expo 2014: Turbine Technical Conference and Exposition; American Society of Mechanical Engineers, 2014; p. V003BT025A015. [Google Scholar]
 Lee, J.J.; Kim, T.S. Development of a gas turbine performance analysis program and its application. Energy 2011, 36, 5274–5285. [Google Scholar] [CrossRef]
 Haglind, F.; Elmegaard, B. Methodologies for predicting the partload performance of aeroderivative gas turbines. Energy 2009, 34, 1484–1492. [Google Scholar] [CrossRef]
 Yang, C.; Huang, Z.; Ma, X. Comparative study on offdesign characteristics of CHP based on GTCC under alternative operating strategy for gas turbine. Energy 2018, 145, 823–838. [Google Scholar] [CrossRef]
 Zhang, G.; Zheng, J.; Yang, Y.; Liu, W. Thermodynamic performance simulation and concise formulas for triplepressure reheat HRSG of gas–steam combined cycle under offdesign condition. Energy Convers. Manag. 2016, 122, 372–385. [Google Scholar] [CrossRef]
 Chen, Q.; Han, W.; Zheng, J.j.; Sui, J.; Jin, H.g. The exergy and energy level analysis of a combined cooling, heating and power system driven by a small scale gas turbine at off design condition. Appl. Therm. Eng. 2014, 66, 590–602. [Google Scholar] [CrossRef]
 Malinowski, L.; Lewandowska, M. Analytical modelbased energy and exergy analysis of a gas microturbine at partload operation. Appl. Therm. Eng. 2013, 57, 125–132. [Google Scholar] [CrossRef]
 Zhang, N.; Cai, R. Analytical solutions and typical characteristics of partload performances of single shaft gas turbine and its cogeneration. Energy Convers. Manag. 2002, 43, 1323–1337. [Google Scholar] [CrossRef]
 Lazzaretto, A.; Toffolo, A. Analytical and neural network models for gas turbine design and offdesign simulation. Int. J. Appl. Thermodyn. 2001, 4, 173–182. [Google Scholar]
 Rowen, W.I. Simplified mathematical representations of heavyduty gas turbines. J. Eng. Power 1983, 105, 865–869. [Google Scholar] [CrossRef]
 Wang, J.; Zhang, C.; Jing, Y. Adaptive PID control with BP neural network selftuning in exhaust temperature of micro gas turbine. In Proceedings of the 2008 3rd IEEE Conference on Industrial Electronics and Applications, Singapore, 3–5 June 2008; pp. 532–537. [Google Scholar]
 Nelson, G.M.; Lakany, H. An investigation into the application of fuzzy logic control to industrial gas turbines. J. Eng. Gas Turbines Power 2007, 129, 1138–1142. [Google Scholar] [CrossRef]
 Panda, S.; Bandyopadhyay, B. Sliding mode control of gas turbines using multirateoutput feedback. J. Eng. Gas Turbines Power 2008, 130, 034501. [Google Scholar] [CrossRef]
 Bonfiglio, A.; Invernizzi, M.; Lanzarotto, D.; Palmieri, A.; Procopio, R. Definition of a sliding mode controller accounting for a reduced order model of gas turbine set. In Proceedings of the 2017 52nd International Universities Power Engineering Conference (UPEC), Crete, Greece, 28–31 August 2017; pp. 1–6. [Google Scholar]
 Bonfiglio, A.; Cacciacarne, S.; Invernizzi, M.; Procopio, R.; Schiano, S.; Torre, I. Gas turbine generating units control via feedback linearization approach. Energy 2017, 121, 491–512. [Google Scholar] [CrossRef]
 Ferrari, M.L. Advanced control approach for hybrid systems based on solid oxide fuel cells. Appl. Energy 2015, 145, 364–373. [Google Scholar] [CrossRef]
 Menon, R.P.; Maréchal, F.; Paolone, M. Intraday electrothermal model predictive control for polygeneration systems in microgrids. Energy 2016, 104, 308–319. [Google Scholar] [CrossRef]
 Zhang, Z.; Zang, S.; Ge, B. Study on multiloop control strategy of threeshaft gas turbine for electricity generation. Aircr. Eng. Aerosp. Technol. 2019, 91, 1002–1010. [Google Scholar] [CrossRef]
 Wu, X.J.; Zhu, X.J. Multiloop control strategy of a solid oxide fuel cell and micro gas turbine hybrid system. J. Power Sources 2011, 196, 8444–8449. [Google Scholar] [CrossRef]
 Sawyer, J.W. Gas Turbine Engineering Handbook; Sawyer, J.W., Ed.; Gas Turbine Publications, 1966. [Google Scholar]
 Jaw, L.C.; Garg, S. Propulsion Control Technology Development in the United States a Historical Perspective; Report; NASA Glenn Research Center: Cleveland, OH, USA, 2005.
 Wall, R. Axial Flow Compressor Performance Prediction; Compressor Research Department RollsRoyce Ltd.: Derby, UK, 1971. [Google Scholar]
 Gallar, L.; Arias, M.; Pachidis, V.; Singh, R. Stochastic axial compressor variable geometry schedule optimisation. Aerosp. Sci. Technol. 2011, 15, 366–374. [Google Scholar] [CrossRef] [Green Version]
 Wang, Z.; Fan, K.; Ma, W.; Li, T.; Li, S. Research on Optimal Matching Method of Variable Stator Vanes for MultiStage Compressor Based on Genetic Algorithm. In Proceedings of the ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition, Oslo, Norway, 11 June 2018. [Google Scholar]
 Kim, S.; Kim, D.; Son, C.; Kim, K.; Kim, M.; Min, S. A full engine cycle analysis of a turbofan engine for optimum scheduling of variable guide vanes. Aerosp. Sci. Technol. 2015, 47, 21–30. [Google Scholar] [CrossRef]
 Kim, S.; Son, C.; Kim, K. Combining effect of optimized axial compressor variable guide vanes and bleed air on the thermodynamic performance of aircraft engine system. Energy 2017, 119, 199–210. [Google Scholar] [CrossRef]
 Hashmi, M.B.; Abd Majid, M.A.; Lemma, T.A. Combined effect of inlet air cooling and fouling on performance of variable geometry industrial gas turbines. Alex. Eng. J. 2020, 59, 1811–1821. [Google Scholar] [CrossRef]
 Martins, D.A.R. OffDesign Performance Prediction of the CFM563 Aircraft Engine. Master’s Thesis, Instituto Superior Técnico, Lisboa, Portugal, 2015. [Google Scholar]
 Silva, O.; Tomita, J.; Bringhenti, C.; Cavalca, D. Hybrid optimization algorithm applied on multistage axial compressor performance calculations with variable geometry. Eng. Optim. 2014 2014, 309. [Google Scholar] [CrossRef]
 Mannarino, G. Control System for Positioning Compressor Inlet Guide Vanes. Google Patents: US Patent 6,735,955, 18 May 2004. [Google Scholar]
 Blair, L.W.; Tapparo, D.J. AxialCentrifugal Compressor Program; General Electric co Lynn ma Aircraft Engine Business Group, 1975. [Google Scholar]
 Garry LaCroix, G.W. Surplus Compression Engine RB21122; Technical Report; Union Gas Limited: Chatham, ON, Canada, 2016; p. 69. [Google Scholar]
 Gadde, S.; Humphrey, C.; Schneider, S.; Tadros, F.; Singh, J. Method of Controlling a Power Generation System. Google Patents: US Patent 7,269,953, 18 September 2007. [Google Scholar]
 Celis, C.; Pinto, P.d.M.R.; Barbosa, R.S.; Ferreira, S.B. Modeling of variable inlet guide vanes affects on a one shaft industrial gas turbine used in a combined cycle application. In Proceedings of the ASME Turbo Expo 2008: Power for Land, Sea, and Air, Berlin, Germany, 9 June 2008; pp. 1–6. [Google Scholar]
 Kurzke, J. About simplifications in gas turbine performance calculations. In Proceedings of the ASME Turbo Expo 2007: Power for Land, Sea, and Air, Montreal, QC, Canada, 14 May 2007; pp. 493–501. [Google Scholar]
 Knopf, F.C. Modeling, Analysis and Optimization of Process and Energy Systems; John Wiley & Sons: Hoboken, NJ, USA, 2011. [Google Scholar]
 Plis, M.; Rusinowski, H. Predictive, adaptive model of PG 9171E gas turbine unit including control algorithms. Energy 2017, 126, 247–255. [Google Scholar] [CrossRef]
 Wirkowski, P. Influence of the incorrect settings of axial compressor inlet variable stator vanes on gas turbine engine work parameters. J. KONES 2012, 19, 483–489. [Google Scholar] [CrossRef]
 Botros, K.; Golshan, H.; Sloof, B.; Samoylove, Z.; Rogers, D. Natural Gas Compressor Operation Optimization to Minimize Gas Turbine Outboard Bleed Air. In Proceedings of the 2012 9th International Pipeline Conference, Calgary, AB, Canada, 24 September 2012; pp. 681–689. [Google Scholar]
 SZUCH, J. Advancements in realtime engine simulation technology. In Proceedings of the 18th Joint Propulsion Conference, Cleveland, OH, USA, 21 June 1982; p. 1075. [Google Scholar]
 Sellers, J.F.; Daniele, C.J. DYNGEN: A Program for Calculating SteadyState and Transient Performance of Turbojet and Turbofan Engines; Techincal Note; National Aeronautics and Space Administration: Cleveland, OH, USA, 1975.
 Koenig, R.W.; Fishbach, L.H. GENENG: A Program for Calculating Design and OffDesign Performance for Turbojet and Turbofan Engines; NASA LEwis Research Center: Cleveland, OH, USA, 1972.
 Geyser, L.C. DYGABCD: A Program for Calculating Linear A, B, C, and D Matrices from a Nonlinear Dynamic Engine Simulation; National Aeronautics and Space Administration: Washington, DC, USA, 1978.
 Visser, W.P.; Broomhead, M.J. GSP A Generic ObjectOriented Gas Turbine Simulation Environment; National Aerospace Labortory (NLR) Based on ASME Turbo Expo 2000: Munich, Germany, 2000. [Google Scholar]
 Macmillan, W. Development of a ModularType Computer Program for the Calculation of Gas Turbine OffDesign Performance. Thesis, Cranfield University, UK, 1974. Available online: http://dspace.lib.cranfield.ac.uk/handle/1826/7401 (accessed on 20 October 2020).
 Palmer, J.; ChengZhong, Y. TURBOTRANS: A programming language for the performance simulation of arbitrary gas turbine engines with arbitrary control systems. In Proceedings of the ASME 1982 International Gas Turbine Conference and Exhibit, London, UK, 18 April 1982; p. V005T014A004. [Google Scholar]
 SADLER, G.; MELCHER, K. DEANA program for Dynamic Engine ANalysis. In Proceedings of the 21st Joint Propulsion Conference, Monterey, CA, USA, 8 May 1985; p. 1354. [Google Scholar]
 Poole, C.; Salsi, A.; Bhinder, F.; Kumar, S. A software environment for the modelling, simulation and control of industrial gas turbine engines. In Proceedings of the ASME 1991 International Gas Turbine and Aeroengine Congress and Exposition, Orlando, FL, USA, 3 June 1991; p. V004T011A006. [Google Scholar]
 Schobeiri, M. AeroThermodynamics of Unsteady Flows in Gas Turbine Systems; BBCTCG51; Brown Boveri Company, Gas Turbine Division Baden Switzerland: Neuchâtel, Switzerland, 1985. [Google Scholar]
 Schobeiri, T. COTRAN, the Computer Code for Simulation of Unsteady Behavior of Gas Turbines; BBCTCG53; Brown Boveri Company, Gas Turbine Division: Baden, Switzerland; Neuchâtel, Switzerland, 1985. [Google Scholar]
 Schobeiri, T. Digital Computer Simulation of the Dynamic Response of Gas Turbines. VDI Annu. J. Turbomach. 1985, 1985, 381–400. [Google Scholar]
 Schobeiri, T.; Haselbacher, H. Transient analysis of gas turbine power plants, using the huntorf compressed air storage plant as an example. In Proceedings of the ASME 1985 International Gas Turbine Conference and Exhibit, Houston, TX, USA, 18 March 1985. [Google Scholar]
 Hale, A.; Davis, M. DYNamic turbine engine compressor code (DYNTECC)theory and capabilities. In Proceedings of the 28th Joint Propulsion Conference and Exhibit, Nashville, TN, USA, 6 July 1992; p. 3190. [Google Scholar]
 Garrard, D. ATEC: The Aerodynamic Turbine Engine Code for the Analysis of Transient and Dynamic Gas Turbine Engine System Operations: Part 1—Model Development. In Proceedings of the ASME 1996 International Gas Turbine and Aeroengine Congress and Exhibition, Birmingham, UK, 10 June 1996. [Google Scholar]
 Kurzke, J. Advanced userfriendly gas turbine performance calculations on a personal computer. In Proceedings of the ASME 1995 International Gas Turbine and Aeroengine Congress and Exposition, Houston, TX, USA, 5 June 1995; p. V005T016A003. [Google Scholar]
 Kurzke, J. GasTurb 12: A Program to Calculate Design and OffDesign Performance of Gas Turbines; User’s Manual: GasTurb: Aachen, Germany, 2012. [Google Scholar]
 Alexiou, A.; Mathioudakis, K. Development of gas turbine performance models using a generic simulation tool. In Proceedings of the ASME Turbo Expo 2005: Power for Land, Sea, and Air, Reno, RenoTahoe, NE, USA, 6 June 2005; pp. 185–194. [Google Scholar]
 Alexiou, A.; Mathioudakis, K. Gas turbine engine performance model applications using an objectoriented simulation tool. In Proceedings of the ASME Turbo Expo 2006: Power for Land, Sea and Air, Barcelona, Spain, 8–11 May 2006. [Google Scholar]
 Bringhenti, C.; Tomita, J.T.; Barbosa, J.R. Gas turbine course’s teaching process at Instituto Tecnológico de Aeronáutica: Theory and laboratory. J. Aerosp. Technol. Manag. 2015, 7, 110–120. [Google Scholar] [CrossRef]
 Schobeiri, M.; Attia, M. Advances in Nonlinear Dynamic Engine Simulation with an Example: Dynamic Performance Behavior of a Gas Turbine with One Reheat Turbine Stage and Two Combustion Chambers. In Proceedings of the ASME 1996 International Gas Turbine and Aeroengine Congress and Exhibition, Birmingham, UK, 10 June 1996. [Google Scholar]
 Gallar, L.; Volpe, V.; Salussolia, M.; Pachidis, V.; Jackson, A. Thermodynamic gas model effect on gas turbine performance simulations. J. Propuls Power 2012, 28, 719–727. [Google Scholar] [CrossRef]
 Rahman, N.U.; Whidborne, J.F. Realtime transient three spool turbofan engine simulation: A hybrid approach. J. Eng. Gas Turbines Power 2009, 131, 051602. [Google Scholar] [CrossRef]
 Visser, W.P.; Broomhead, M.J.; van der Vorst, J. TERTS: A generic realtime gas turbine simulation environment. In Proceedings of the ASME Turbo Expo 2001: Power for Land, Sea, and Air, New Orleans, LA, USA, 4 June 2001. [Google Scholar]
 Blendulf, L.J.; Smith, G.D. Design Point Simulation of Multispool Industrial Compressor Trains. In Proceedings of the ASME 1994 International Gas Turbine and Aeroengine Congress and Exposition, The Hague, The Netherlands, 13 June 1994. [Google Scholar]
 Frith, P. An Openloop Transient Thermodynamic Model of the Couguar Turbojet; AERONAUTICAL RESEARCH LABS MELBOURNE: Melbourne, Australia, 1989.
 Guan, Y.S.; Warng, J.S.; Lee, T.C. A new method of digital simulation for an aircraft gas turbine engine control system. Appl. Math. Model. 1987, 11, 458–464. [Google Scholar] [CrossRef]
 BayonaRoa, C.; SolísChaves, J.; Bonilla, J.; RodriguezMelendez, A.; Castellanos, D. Computational Simulation of PT6A Gas Turbine Engine Operating with Different Blends of Biodiesel—A TransientResponse Analysis. Energies 2019, 12, 4258. [Google Scholar] [CrossRef] [Green Version]
 Gazzetta Junior, H.; Bringhenti, C.; Barbosa, J.R.; Tomita, J.T. Realtime gas turbine model for performance simulations. J. Aerosp. Technol. Manag. 2017, 9, 346–356. [Google Scholar] [CrossRef]
 Thirunavukarasu, E. Modeling and Simulation Study of a Dynamic Gas Turbine System in a Virtual Test Bed Environment. Thesis, University of South Carolina, Columbia, SC, USA, 2013. Available online: https://scholarcommons.sc.edu/etd/2254 (accessed on 20 October 2020).
 Sethi, V.; Doulgeris, G.; Pilidis, P.; Nind, A.; Doussinault, M.; Cobas, P.; Rueda, A. The map fitting tool methodology: Gas turbine compressor offdesign performance modeling. J. Turbomach. 2013, 135, 061010. [Google Scholar] [CrossRef]
 dos Santos Silva, F.J.; Bringhenti, C.; Barbosa, J.R. Transient performance of gas turbines. In Proceedings of the 18th International Congress of Mechanical Engineering, Ouro Preto, Brazil, 6 November 2005. [Google Scholar]
 Tacconi, J. Investigation of a SemiClosed Cycle Small Gas Turbine for High Altitude UAV Propulsion. Master’s Thesis, TU Delft, Delft, The Netherlands, 2018. [Google Scholar]
 Chung, G.Y.; Prasad, J. Turbofan Engine Transient Response Predictions Using RealTime Analytical Linear Models. In Proceedings of the 50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Cleveland, OH, USA, 28 July 2014; p. 3926. [Google Scholar]
 Argote, C.; Kestner, B.K.; Mavris, D.N. NPSS Volume Dynamic Capability for RealTime Physics Based Engine Modeling. In Proceedings of the ASME 2011 Turbo Expo: Turbine Technical Conference and Exposition, Vancouver, BC, Canada, 6 June 2011; pp. 139–148. [Google Scholar]
 Lytle, J.K. The Numerical Propulsion System Simulation: An Overview; NASA Glenn Research Center: Cleveland, OH, USA, 2000.
 Jones, S.M. Steadystate modeling of gas turbine engines using the Numerical Propulsion System Simulation code. In Proceedings of the ASME Turbo Expo 2010: Power for Land, Sea, and Air, Glasgow, UK, 14 June 2010; pp. 89–116. [Google Scholar]
 Claus, R.; Evans, A.; Follen, G. Multidisciplinary propulsion simulation using NPSS. In Proceedings of the 4th Symposium on Multidisciplinary Analysis and Optimization, Cleveland, OH, USA, 1 January 1992; p. 4709. [Google Scholar]
Author  Year  Variable Geometry Features  

VIGVs or VSVs  Variable Bleed  NGVs or VGVs for PT  
Mohammadian and Saidi, [56]  2019  ✓  ✓  
MontazeriGh et al. [57]  2018  ✓  
Schobeiri, [58]  2018  ✓  
Mehrpanahi et al. [34]  2018  ✓  
Wang et al. [59]  2018  ✓  
Silva et al. [60]  2018  ✓  
Wang et al. [61]  2018  ✓  
Enalou, [62]  2017  ✓  
MontazeriGh, [63]  2017  ✓  
Wang et al. [43]  2017  ✓  
Kim et al. [45]  2016  ✓  
Kim et al. [64]  2015  ✓  ✓  
Barbosa et al. [65]  2012  ✓  
Chacartegui et al. [66]  2011  ✓  
Barbosa et al. [67]  2011  ✓  
Panov et al. [68]  2009  ✓  
Silva et al. [69]  2007  ✓  
Sekhon et al. [36]  2006  ✓  
Bringhenti et al. [70]  2006  ✓  ✓  ✓ 
Camporeale et al. [71]  2006  ✓  
Kim et al. [72]  2001  ✓  
Kim et al. [73]  2001  ✓  
Kim and Soudarev, [74]  2000  ✓  
Blanco and Henricks, [75]  1998  ✓  
Boumedmed, [76]  1997  ✓  
Perretto, [77]  1997  ✓  
Bettocchi et al. [33]  1996  ✓  
Nava et al. [78]  1995  ✓  
MehrHomji and Bhargava, [39]  1992  ✓ 
Method  Researchers  Respective Equations  Benefits  Overall Drawbacks 

Map Scaling Method  [68,149,151,152,153]  $PR=\frac{{\left(PR\right)}_{design}1}{{\left(PR\right)}_{map,design}1}\left[{\left(PR\right)}_{map}1\right]+1$ $\dot{m}=\frac{{\dot{m}}_{design}}{{\dot{m}}_{map,design}}\times {\dot{m}}_{map}$ $\eta =\frac{{\eta}_{design}}{{\eta}_{map,design}}\times {\eta}_{map}$  1. Quite easy and simplest method to develop compressor map 2. Time saving  1. Not Applicable for variable geometry compressor 2. Limitation in selection of reference map 3. Not accurate for offDesign operation 4. This method overlooks the compressibility factor 
Sequential Stage Stacking method  [137]  Flow coefficient, $\varphi =\frac{{C}_{x}}{u}$ Pressure Coefficient, $\psi ={C}_{P}{T}_{t,in}\left(P{R}_{s}^{\frac{\gamma 1}{\gamma}}1\right)/{U}^{2}$ Temperature Rise,$\xi =\frac{{C}_{p}\Delta {T}_{t}}{{U}^{2}}$ Stage Efficiency, $\eta =\frac{\psi}{\xi}$  1. Accurate performance prediction 2. Applicable for both fixed and variable geometry compressors  1.Problem in off design operations 2. problems during stalling and choking 3. Time consuming 4. It requires Gas path geometric data like stage mean radius and annulus area that are not provided by manufacturer 
Modified Stage Stacking Method  [154]  ${\dot{m}}_{i+1}={\dot{m}}_{i}$ ${\dot{m}}_{i+1}{C}_{{x}_{i+1}}+{P}_{i+1}{A}_{i+1}={\dot{m}}_{i}{C}_{{x}_{i}}+{P}_{i}{A}_{i}+{F}_{s}$ ${\dot{m}}_{i+1}{H}_{{t}_{i+1}}={\dot{m}}_{i}{H}_{{t}_{i}}+{\dot{W}}_{s}$  1. Flexibility in boundary conditions 2. Time saving calculations due to simultaneous solutions 3. Variable geometry treatment by variation in setting angle 4. Applicable for transient modeling due to stability in numerical methods  1.Gas path geometric data like stage mean radius and annulus area are not provided by Manufacturer 2. Unavailability of reference data at Max efficiency 
[12,72,73,90,155,156]  ${\psi}^{*}={\psi}_{Max}^{*}\frac{{\psi}_{Max}^{*}1}{{\left({\varphi}_{\psi}^{*}{}_{Max}1\right)}^{2}}\times {\left({\varphi}_{\psi}^{*}{}_{Max}{\varphi}^{*}\right)}^{2}$ ${\eta}_{Min}^{*}=1\frac{1{\eta}_{{\left(\frac{\psi}{\varphi}\right)}_{Min}}^{*}}{{\left[1{\left(\frac{{\psi}^{*}}{{\varphi}^{*}}\right)}_{Min}\right]}^{3.5}}{\left(1\frac{{\psi}^{*}}{{\varphi}^{*}}\right)}^{3.5},where\frac{{\psi}^{*}}{{\varphi}^{*}}\in \left[{\left(\frac{{\psi}^{*}}{{\varphi}^{*}}\right)}_{Min},1\right]$ ${\eta}_{Max}^{*}=1\frac{1{\eta}_{{\left(\frac{\psi}{\varphi}\right)}_{Max}}^{*}}{{\left[{\left(\frac{{\psi}^{*}}{{\varphi}^{*}}\right)}_{Max}1\right]}^{3.5}}{\left(\frac{{\psi}^{*}}{{\varphi}^{*}}1\right)}^{2},where\frac{{\psi}^{*}}{{\varphi}^{*}}\in \left[1,{\left(\frac{{\psi}^{*}}{{\varphi}^{*}}\right)}_{Max}\right]$  Thermodynamic cycle program combined with performance maps generated through stage stacking helps in searching the operating point values (thermodynamic performance parameters) like compressor PR, SFC and TET that is not possible in the rest of the methods  The Minimization Algorithm adopted in this method is not stable for large number of unknowns. So a robust technique i.e., Genetic Algorithm is suggested for future work  
Blade Element Method  [75,157,158]  $\Delta {h}_{t}=({U}_{2}^{2}{U}_{2}{C}_{x2}\mathrm{tan}{\beta}_{2}{U}_{1}{C}_{x1}\mathrm{tan}{\alpha}_{1})/{g}_{c}$ $\overline{\omega}=\frac{{P}_{t1}{P}_{t2}}{{P}_{t1}{P}_{1}}$ ${C}_{D}=\frac{\overline{\omega}}{\sigma}\left(\frac{{\mathrm{cos}}^{3}{\alpha}_{m}}{{\mathrm{cos}}^{2}{\alpha}_{1}}\right),Where\mathrm{tan}{\alpha}_{m}=\left(\frac{\mathrm{tan}{\alpha}_{1}+\mathrm{tan}{\alpha}_{2}}{2}\right)$  1. Little dependency on the cascade data 2. Applicable for variety of stages of compressors according to the desired compressor 3. Holds good for VIGV adjustment due to simulation of each blade element  The loss and deviation correlation curves obtained from the literature are not robust in terms of accuracy 
Turbine Modeling Methods  Respective Mathematical Expression  Significance 

Choking Equation  $\frac{{\dot{m}}_{in}\sqrt{{T}_{in}}}{\kappa A{P}_{in}}=Constant$ Where $\kappa =\sqrt{\frac{\gamma}{R}}{\left(\frac{2}{\gamma +1}\right)}^{\frac{\gamma +1}{\gamma 1}}$ 

Stodola Ellipse Equation  $\frac{{m}_{in}\sqrt{{T}_{Tin}}}{{P}_{in}}=K\text{}\sqrt{1{\left(\frac{{P}_{out}}{{P}_{in}}\right)}^{2}}$  Useful for estimating turbine characteristics during off design condition 
Flugel Formula  $\frac{{m}_{in}}{{m}_{in,ref}}=\frac{\sqrt{{\left({p}_{in}{p}_{out}\right)}^{2}}}{\sqrt{{\left({p}_{inref}{p}_{outref}\right)}^{2}}}\times \frac{\sqrt{{T}_{inref}}}{\sqrt{{T}_{in}}}\text{}$  Gives a correlation of mass flow, pressure and temperature for turbine in off design condition 
Researcher  Correlations  Correction Factors 

Celis et al. [193]  Mass flow ${\left[\frac{\left(\frac{\dot{m}}{{p}_{in}}\times \frac{\sqrt{R{T}_{in}}}{\gamma}\right)}{{\left(\text{}\frac{\dot{m}}{{p}_{in}}\times \frac{\sqrt{R{T}_{in}}}{\gamma}\right)}_{DP}}\right]}_{VIGV}=a{\left[\frac{\left(\frac{\dot{m}}{{p}_{in}}\times \frac{\sqrt{R{T}_{in}}}{\gamma}\right)}{{\left(\text{}\frac{\dot{m}}{{p}_{in}}\times \frac{\sqrt{R{T}_{in}}}{\gamma}\right)}_{DP}}\right]}_{n}$ Pressure ratio ${\left[\frac{\frac{{p}_{out}}{{p}_{in}}1}{{\left(\frac{{p}_{out}}{{p}_{in}}1\right)}_{DP}}\right]}_{VIGV}=b\text{}{\left[\frac{\frac{{p}_{out}}{{p}_{in}}1}{{\left(\frac{{p}_{out}}{{p}_{in}}1\right)}_{DP}}\right]}_{n}$ Efficiency ${\left[\frac{\eta}{{\left(\eta \right)}_{DP}}\right]}_{VIGV}=c\text{}{\left[\frac{\eta}{{\left(\eta \right)}_{DP}}\right]}_{n}$  Correction factor a, b and c represents change in mass flow, pressure ratio and efficiency, respectively. 
Kurzke, [194]  ${\dot{m}}_{VIGV}={\dot{m}}_{FG,map}\times \left(1+\frac{{c}_{1}\Delta {\theta}_{VIGV}}{100}\right)\text{}$ ${\left(PR1\right)}_{VIGV}={\left(PR1\right)}_{FG,map}\times \left(1+\frac{{c}_{2}\Delta {\theta}_{VIGV}}{100}\right)$ ${\eta}_{VIGV}={\eta}_{FG,map}\times \left(1\frac{{c}_{3}\Delta {\theta}_{VIGV}^{2}}{100}\right)$  ${c}_{1}$,$\text{}{c}_{2}$,$\text{}{c}_{3}$ 
Knopf, [195]  Mass flow correction ${\dot{m}}_{OD}={\dot{m}}_{DP}\times \frac{{P}_{1,OD}}{{P}_{1,DP}}\times \frac{{T}_{1,DP}}{{T}_{1,OD}}\left({K}_{V}\Delta {\theta}_{VIGV}\right)\left[1+{K}_{T}\left(\frac{{T}_{1,OD}{T}_{1,DP}}{{T}_{1,DP}}\right)\text{}\right]$ Efficiency correction ${\eta}_{OD}={\eta}_{Max}\left(1\left\frac{{\dot{m}}_{DP}{\dot{m}}_{OD}}{{\dot{m}}_{DP}}\right\left({K}_{m}\right)\right)\left[1+{K}_{E}\left\frac{{N}_{OD}{N}_{Max,\eta}}{{N}_{Max,\eta}}\right\right]$  ${K}_{V}$,$\text{}{K}_{T}$,$\text{}{K}_{m}$,$\text{}{K}_{E}$ 
Plis and Rusinowski, [196]  Mass flow correction ${\dot{m}}_{VIGV}={\dot{m}}_{VIGV,Max}\left[1{K}_{V}\left({\theta}_{VIGV,Max}{\theta}_{VIGV}\right)\right]$ Efficiency empirical correlation developed from Wirkowski’s [197] experimental data ${\eta}_{VIGV}={\alpha}_{0}+{\alpha}_{1}\xb7{\dot{m}}_{corr}+{\alpha}_{2}\xb7{\dot{m}}_{corr}^{2}+{\alpha}_{3}\xb7{N}_{corr}+{\alpha}_{4}\xb7{N}_{corr}^{2}+{\alpha}_{5}\xb7{\dot{m}}_{corr}\xb7{N}_{corr}+{\alpha}_{6}\xb7{\theta}_{VIGV}+{\alpha}_{7}\xb7{\theta}_{VIGV}^{2}+{\alpha}_{8}\xb7{\dot{m}}_{corr}\xb7{\theta}_{VIGV}+{\alpha}_{9}\xb7{N}_{corr}\xb7{\theta}_{VIGV}$  ${K}_{V}$ 
Software  Developer/Owner  Type  Variable Geometry  Range of Flexibility  Pros  Cons  Reason for Utilization in Various Studies 

GasTurb  Dr. Joachim Kurzke  0 D, OOP  VIGV + Bleed schedule  1. Turbomachinery fouling and erosion, 2. Inlet flow distortion, 3. Optimization, 4. MonteCarlo  1. Need limited information from user, 2. User friendly for the GT operators due to predefined engine configuration  The model cannot be saved and transferred. For some cases it is very hard to import excel file, VIGV schedule only with respect to speed  Validation [43,50,145,226,227,228] 
GSP  National Aerospace Laboratory NLR, Netherlands  0D, OOP  VIGV +Bleed schedule  Turbomachinery fouling and erosion, shaft dynamics,  1. Easy saving and transporting of the model to other PCs, 2. Effects of ambient and flight conditions, installation losses, and malfunctions of control can be simulated  It is not user friendly for the gas turbines operators because its need every detail from the user even configuration need to be structured by user  Validation [44,49,222] 
PROOSIS  Alexiou from National Technical University of Athens  1D, OOP  No VIGV and Bleed  Parametric study, Optimization, Diagnostics  1. Model adaptation to specific engine using measured data 2. Frequency response analysis can be performed 3. Availability of extra auxiliary components such as gear box, generator and propeller  creation of libraries in the EL language require good expertise in the mathematical formulation of the components that limit this software to only academic community not to operators  validation [9,23,45,229] 
GTAnalysis  Gas Turbine Group, ITA, Brazil  Modular with interactive block structuring  VIGV and Bleed schedule, VAN for turbines  Deterioration  Due to its modular characteristic, any required modification can be easily incorporated to the program, making it very friendly  For variable geometry effect study, another in house program AFCC need to utilize  Modeling [14,60,69,70,230] 
NPSS  NASA Glenn Research Center  multiD  No  1. Integration of components for large systems and subsystems 2. effects of aerothermal and structural loadings on geometry and efficiency can be simulated  1. Additional codes can be appended 2. Zooming can give more details of the component performance inside the engine 3. High fidelity variable complexity analysis can be performed during design problems  Only available to partner research institutes of NASA  Modeling [184,231,232,233] 
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Hashmi, M.B.; Lemma, T.A.; Ahsan, S.; Rahman, S. Transient Behavior in Variable Geometry Industrial Gas Turbines: A Comprehensive Overview of Pertinent Modeling Techniques. Entropy 2021, 23, 250. https://doi.org/10.3390/e23020250
Hashmi MB, Lemma TA, Ahsan S, Rahman S. Transient Behavior in Variable Geometry Industrial Gas Turbines: A Comprehensive Overview of Pertinent Modeling Techniques. Entropy. 2021; 23(2):250. https://doi.org/10.3390/e23020250
Chicago/Turabian StyleHashmi, Muhammad Baqir, Tamiru Alemu Lemma, Shazaib Ahsan, and Saidur Rahman. 2021. "Transient Behavior in Variable Geometry Industrial Gas Turbines: A Comprehensive Overview of Pertinent Modeling Techniques" Entropy 23, no. 2: 250. https://doi.org/10.3390/e23020250