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EXAMPLE 9.3 A turbofan engine has a fan and a low-pressure compressor driven by the low- pressure turbine, as shown in Figure 9.31. It operates at a flight velocity of 200 m/s at 12,000 meters altitude, where the ambient temperature and pressure are 216.65K and 0.1933 bar, respectively. The overall pressure ratio the engine is 19, and the fan and low-pressure-compressor pressure ratios are 1.65 in 2.5, respectively. The fan, compressors, and turbines have 90% polytropic efficiencies. Assume an isentropic inlet and separate isentropic convergent nozzles, a fuel heating value of 43,000 kJ/kg, and a combustor total pressure loss of 6.5%. Determine the core engine and bypass duct exit velocities, the engine thrust specific fuel consumption, thrust, and specific thrust for an engine with an inlet air flow of 100 kg/s and a bypass ratio of 3.0. Determine whether the nozzles are choked. Solution Table 9.6 tabulates, in spreadsheet format, the design data for the example and systematically calculates the engine parameters. After computing the fan and LP- turbine exit total pressures, the nozzles may be checked for choking at the throats. The applied pressure ratios are compared with the critical pressure ratios for cold bypass air (k = 1.4) and for hot gas (k = 4/3), respectively. Branching in the computation required by the presence or absence of choking is easily handled by the @IF function of popular spreadsheets, which allows a conditional selection between specified alternatives, as discussed previously in connection with Example 5.6. TABLE 9.6 Spreadsheet Solution to Example 9.3 AEROTHERMODYNAMIC ANALYSIS OF A FANJET Ca Ta Pa Fuel HV Cpa Cpa/Cpg OPR FPR LPCPR HPCPR B mair cpeta (n-1)/n l comp 200 m/s 216.65 K 0.1933 Bar 43000 kJ/kg 1.005 kJ/kg 0.8754 19.0000 1.6500 2.5000 4.6100 3.0000 100 kg/s 0.9 0.3175 Flight velocity Ambient temperature Ambient pressure Heating value Air heat capacity Air/gas heat capacity ratio Overall pressure ratio Fan pressure ratio Low pressure compressor pressure ratio HPCPR = OPR/[(FPR)(LPCPR)] Bypass Ratio Inlet total mass flow rate Compressor and fan polytropic efficiencies (n-1)/n = (k-1)/[kCcpeta] (for fan & comp.) 380PDF Image | Advanced Systems Steam Power Plant
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