THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 345 E. 47th St, New York, N.Y. 10017 987G117172 , The Society shall not be responsible tor statements or opinions advanced in papers or discussion at meetings of the Sodety or of fts Divisions or Sections, or printed in its publications. Discussion is printed only if the paper is published in an ASME Journal. Authorization to photocopy for internal or personal use is granted to libraries and other users registered with the Copyright Clearance Center (CCC) provided S3/article or S4/page is paid to CCC, 222 Rosewood Dr., Danvers, MA 01923. Requests for special permission or bulk reproduction should be addressed to the ASME Technical Publishing Department. Copyright 0 1998 by ASME All Rights Reserved Printed in U.SA. • DYNAMIC MODELING AND CONTROL OF REGENERATIVE GAS TURBINES S.M. Camporeale * , B. Fortunato n , A. Dumas" * Dipartimento di Meccanica dei Fluidi a Ing. Off-shore, Universita di Reggio Calabria, Contrada Feo di Vito, Reggio Calabria, 89128, Italy • * Istituto di Macchine ed Energetica, Politecnico di Bari, 1111111111 11a1111111111 via Re David 200, Bari, 70125, Italy ABSTRACT A non linear dynamic model has been developed in order to simulate the dynamic behavior of single-shaft or multi-shaft regenerative gas turbines. The aim of the work is to provide a fast and reliable model for the synthesis of the controllers and the study of critical dynamic situations. Some significant features characterize the proposed model: – an efficient one-dimensional model is used in order to properly model a stationary counter-flow regenerator; – a stage by stage model is provided for the air cooled turbine expansion in order to take into account the blade thermal transients. The mathematical model and the numerical methodology are described in the paper. A single-shaft regenerative cycle gas turbine is analyzed. In order to design a multivariable controller for this plant, a linearized model is developed from the non-linear model. The gas turbine is described by the transfer functions that relate the input variables (fuel rate and variable inlet guide vanes) to the state variables (shaft speed and turbine output temperature). Accuracy and effects of non-linearities are described. NOMENCLATURE A = heat transfer area • = heat capacity rate of the fluid = mass flow rate x specific heat C - = fixed capacity • = specific heat capacities • = internal energy It = enthalpy 14 = lower heating value = moment of inertia, kg m 2 k = cdc„ • = orifice coefficient • = total flow length of the heat exchanger = mass flow rate, kg/s • = Mach number nb, = number of blades per row • = Number of Thermal Units • = stagnation pressure • = static pressure • = power , W = time, s d = dwell time of the cold flow in the heat exchanger • = stagnation temperature • = turbine outlet temperature, K • = peripheral velocity • = global heat transfer coefficient, • = velocity component in axial direction V = volume = parameter of the loss of momentum • = work per mass unit Greek a = convection heat transfer coefficient fi = pressure ratio s = heat transfer efficiency ▪ = aerodynamic load coefficient • = density re = rotational speed, red's O = annular flow area Subscripts = inlet section 2 = outlet section a = air Presented at the International Gas Turbine & Aemengine Congress & Exhibition Stockholm, Sweden — June 2–June 5,1998 Downloaded from https://asmedigitalcollection.asme.org/GT/proceedings-pdf/GT1998/78668/V005T15A019/4219068/v005t15a019-98-gt-172.pdf by guest on 19 July 2020