Performance estimation of some variable bypass ratio turbofan engines

This paper presents basic performance analysis of two types of turbofan engines with variable area in the turbine section: (1) separate exhaust turbofan engine with variable area between the high and low pressure turbine and (2) mixed flow turbofan engine with variable area mixer. Using basic concepts, a fundamental understanding of engine cycle analysis is obtained which helps both student understanding and predicting the performance of the new variable cycle gas turbine engines under development Nomenclature Aj Row area at engine station i CTC Specific heat at constant pressure upstream of combustor c t Specific heat at constant pressure downstream of combustor f Fuel-to-air ratio Mass flow rate of core stream Mass flow rate of fan stream rii; Mass flow rate at engine station i Mj Free stream Mach number at engine station i MFP Mass Flow Parameter Pti Total pressure at engine station i Tti Total temperature at engine station i Greek a Engine bypass ratio Yc Ratio of specific heats upstream of combustor Yt Ratio of specific heats downstream of combustor 7Ccjj High pressure compressor total pressure ratio ( = 7tcL Low pressure compressor total pressure ratio ( = 7Cf Fan total pressure ratio ( = Ptl3/P,2) 7tt Turbine total pressure ratio ( = P^ Pt4 ) TCjjj High pressure turbine total pressure ratio ( = P{4 g/ P{4 ) TCjL Low pressure turbine total pressure ratio ( = P^ Pt4 5 ) TJ cH High pressure compressor efficiency T| cL Low pressure compressor efficiency High pressure spool mechanical efficiency Low pressure spool mechanical efficiency t Senior Member AIAA, Associate Professor T| jjj High pressure turbine efficiency T| Low pressure turbine efficiency tcH High pressure compressor total temperature ratio ( = T^ TcL Low pressure compressor total temperature ratio ( = T^ Tj Fan total temperature ratio ( = Ttl3/ T^ ) Tt Turbine total temperature ratio ( = 1^/7^) TJJJ High pressure turbine total temperature^ratio ( = Tt4y Tt4 ) T^ Low pressure turbine total temperature ratio ( = T^/ T{4 5 ) Subscript R Reference engine condition 0-19 Engine station number Introduction This article uses the cycle analysis methods first introduced by Frank E. Marble of the California Institute of Technology and further developed by Gordon C. Gates (Ref. 1) of the University of Washington and Jack L. Kerrebrock (Ref. 2) of the Massachusetts Institute of Technology. The material presented here builds directly upon this author's work published in Aircarft Engine Design (Ref. 3) and Elements of Gas Turbine Propulsion (Ref. 4). The station numbering used in this analysis is based on the industry standard contained in Aerospace Recommended Practice (ARP) 755A (Ref. 5). A cross-sectional view of a separate exhaust turbofan engine is shown in Figure 1 and that of a mixed flow turbofan engine is shown in Figure 2. The high pressure turbine (between stations 4 and 4.5) drives the high pressure compressor (between stations 2.5 and 3). The low pressure turbine (between stations 4.5 and 5) drives both the low pressure compressor (between stations 2 and 2.5) and the fan (between stations 2 and 13). Turbine Characteristics Before developing the equations that predict the operating characteristics of the turbine, we write the mass flow parameter at any station "i" in terms of mass flow rate, total pressure, total temperature, area, and Mach number. = MFP(MO = For a turbojet engine, the flow is choked (M = 1) in the turbine inlet guide vanes (station 4) and nearly at the throat of the exhaust nozzle (station 8). Thus the corrected mass flow rate-per-unit area is constant at station 4 and n^ = I^A± MFP(M4) rh8 = M MFP(M8) (i) VTt4 VTt8 For the simple turbojet engine shown in Figure 3, the mass flow rate through the turbine is equal to that through the exhaust nozzle or Using Eq. (i) for a single spool engine, then VT t8/T t4 = A8 MFP(M8) Pt8/Pt4 A4 MFP(M4) or Tt 7Ct = A8 MFP(M8) A4 MFP(M4) (la)