|Fig. 1: Thermal Efficiency of the ideal Brayton cycle as a function of the pressure ratio, for a cycle where the working fluid of air is modeled as an ideal gas with constant specific heat ratio γ=1.4. The efficiency is η = 1 - (1/rp)(γ-1)/γ  (Source: J. Ginsberg)|
The Brayton cycle generalizes the operation of gas turbine engines and consists of four processes: adiabatic compression, isobaric combustion, adiabatic expansion, and isobaric heat rejection. Idealized, the Brayton cycle describes the generation of fast moving fluid for thrust in jet propulsion and, more directly, dictates the relationship between thermal efficiency and pressure ratio, rp. For fixed values Tmax and Tmin, the net work out of the brayton cycle first increases with the pressure ratio then reaches a maximum at rp = (Tmax/Tmin)γ/[(γ-1)], with γ = cp/cv, where cp and cv are contant-pressure and constant-volume molar specific heats (see Fig. 1). This has significant consequences for fuel economy as continued improvements in engine pressure ratios will have a diminishing effect on thermal efficiency, unless new materials capable of handling higher temperatures are developed. 
More than any other form of transportation, aviation depends on efficiency to lower costs and increase range. While reducing drag, modifying wing tip design, lightening components, and electrifying auxiliary power units provide alternative means of increasing fuel economy, engine efficiency remains the most significant pressure point. Jet fuel accounts for 40% of airline operating costs and represents 3% of global fossil fuel usage. 
But improving engine efficiency is not straightforward. Jet engine efficiency has two components: one thermodynamic, the other propulsive. The thermodynamic component accounts for the percentage of chemical energy of fuel converted to the kinetic energy of the air moving through the turbine. The propulsive comprises the percentage of kinetic energy that provides actual thrust. Simply increasing fan size to increase air flow and thermodynamic efficiency for example would come at a cost to drag, weight, and aerodynamic efficiency.  Similarly, increasing propulsive efficiency by raising operating temperature would result in higher NOx emissions, the need for more heat-resistant materials, and a greater level of cooling flows.
|Fig. 2: Diagram high-bypass turbofan engine, with LP spool in green and HP spool in purple. (Source: Wikimedia Commons)|
As the number of aircraft in service is expected to double by 2040, the severity of engine inefficiencies will only magnify. Though today's Boeing 737 compared to the original 1967 model carries 48% more passengers 119% further with 23% less fuel, more recent advances have tapered off as dictated by the Brayton cycle. 
The most significant improvement to fuel consumption in recent years has been the adoption of high-bypass turbofan engines, first developed in 1941. In a turbofan engine, mechanical energy from the engine turbine drives a ducted fan to thrust air rearwards (Fig. 2). The turbine and fan work in tandem, with a higher bypass ratio reflecting that the fan provides more thrust than the core section. Since less air flow in the core means less fuel usage needed to provide thrust, efficiency improves with higher bypass ratio. Though this efficiency depends on the airspeed of the exhaust to the surrounding air, turbofan engines have greatest propulsive efficiency between 500 and 1000 km/h, the typical range of commercial aircraft.  Though a higher bypass ratio means a larger and heavier engine, the efficiency and cost balance has become worthwhile for manufacturers.
|Fig. 3: General Electric GEnx turbofan engine with its cowl open. (Source: Wikimedia Commons)|
The latest development of GE Aviation reflects the balance and culmination of these technical improvements. The GEnx-2B67 is an advanced dual rotor, axial flow, high-bypass turbofan engine for use by the Boeing 747-8 and 787 Dreamliner aircraft (Fig. 3). Notably, the GEnx-2B67 obtains an overall pressure ratio of 44.7 at sea level T-O, operating well above the ratios of the CF6 and GE90 engines currently in production (OPR < 40).  And has an over 20% fuel consumption improvement over the ubiquitous PW 4000 engine. Additionally, the 2B67 eliminates bleed air systems in favor of electrifying traditionally hydraulic and pneumatic anti-ice and air conditioning systems. Most importantly, the 2B67 reduces fuel consumption by obtaining a high bypass ratio of 9.6:1 and compression ratio of 23:1. Since the 2B67 favors propulsive efficiency, several components have been implemented to counteract inherent deficiencies: the introduction of cooling techniques to reduce internal engine temperatures, advanced composite materials to reduce weight, and a lean twin annular premixed swirler combustor to reduce NOx emissions by 40%. All of these yield a fuel burn 15% better than GE's current CF6 and a thrust of 67,000 lbs.  Though the National Transportation Safety Board has publicly announced reservations about the safety of the new engines, GE expects to produces hundreds in the coming years.  These new engines will represent perhaps the apex of current jet engine technology, before pressing demand and physical limitations require the development of new, more computationally optimized and materially sophisticated engine designs.
© Jason Ginsberg. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
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