Jet Engine

Description

Jet engines are devices using a gas turbine for converting chemical energy into work in the form of kinetic energy of a stream of air. The change of momentum of the air jet is used to propel the aircraft forwards.

Characterisation

There are three main designs of jet engine turboprop, turbofan and turbojet, which differ in the design by-pass ratio: the share of air which is not passed through the combustor.

Turboprops are used for small aircraft that fly at low Mach numbers, turbofans are used for most commercial flight applications while turbojets are only used for military applications.

The turbofan design has the highest bypass ratio and efficiency of all [292]. Jet engines are

rated by thrust rather than by power, and to convert from one to another flight conditions must be assumed.

Efficiency measure

The overall efficiency of Jet Engine is defined as the ratio between the input chemical energy (in LHV terms) and the produced kinetic energy.

ηo= ∆ ˙E_k

˙

m_fLHV (4.17)

However, the aviation industry uses different definitions of efficiency the thrust specific fuel consumption (tsfc), which needs to be manipulated in order to obtain an efficiency value in the desired form

The tsfc is a measure of the efficiency of the engine computed as the mass flow of fuel required to generate one unit of thrust. This measure can be used to understand the overall engine efficiency by making a few assumptions using the following equation, where V is the cruise speed and LHV is the fuel’s lower heating value.

η_o= V

tsfcLHV (4.18)

Key Parameters

Thermal Efficiency The thermal efficiency is only dependent on the core design, which has the design of a gas turbine, and has already been discussed in section 4.2.1. The main difference in the design parameters, the core of jet engines and land based gas turbine are the inlet conditions. At cruise conditions at 10 600 m (35 000 ft), the standard atmospheric conditions are: T = 216 K and P = 0.226 bar [307].

Transfer Efficiency The transfer efficiency represents the efficiency with which the work generated by the core can be turned in kinetic energy. Most of the losses incurred in this process, are due to the pressure loss of the bypass flow on the nacelle wall as well as other internal entropy generation mechanisms [308]. According to Rollys Royce engineers, current state of the art engines are designed with transfer efficiencies of 85% [309].

Propulsive Efficiency The propulsive efficiency is a function of the engine’s architecture and can be expressed as

η_propulsive= 2V

V+V_J (4.19)

where V_J is the jet velocity. If all of the engine’s power is transferred to a jet, then that would result in a high velocity jet. On the other hand, by using a fraction of the core’s power to run a fan with a much lower pressure ratio but much larger air flow rate, it is possible to lower the jet velocity and thus increase the propulsive efficiency. Current high bypass ratio designs reach values up to 10, as in the GE90. This value translate to propulsive efficiencies of about 80% [309].

Efficiency Limits Literature estimates

Parker in a 2006 review of jet engine technologies [310], states that there is a 30% im-provement potential between the high bypass ratio engines from the early 2000s and the theoretical limit. He states that the theoretical limit of propulsive efficiency is 92.5%, which the propulsive efficiency of open rotor technology. He also states that the practical limit to thermal efficiency is 55% while the theoretical limit is 60%. The first can be reached within NO_xlimitations, while the latter represents the efficiency of stoichiometric combustion tem-perature, ultimate aerodynamic efficiency and pressure ratios above 80. Therefore according to Parker, the technical efficiency limit of jet engines is 55.5%.

In an initial assessment of Open Rotor technology [311], NASA presented engine design simulation results for an advanced geared open rotor engine. Even though there is no mention of this being an engine designed at the technical limits, the design characteristics encompass all of the available technologies. Their simulation yields a tsfc of 11.1 g/kNs which is equivalent to an overall efficiency of 50.6%.

Physical model

The physical model of the jet engine is based on the model described for gas turbines in section 4.2.1. In addition, other kinetic energy losses, described as the propulsive and transfer efficiency, are added to better represent the device.

The overall efficiency of the engine is composed of the core’s thermal efficiency, the efficiency with which mechanical energy is transferred to kinetic energy and the engine’s propulsive

efficiency.

η_overall= ηthermal× ηtrans f er× ηpropulsive

= E_core

E_{f uel} ×E_jets− E_inlet

E_core × FV

E_jets− E_inlet where E is the energy, F is the thrust and V is the cruise velocity.

Efficiency limit estimation

The efficiency limit is estimated using methodology A. The rationale and references behind each estimation are presented in this section.

Thermal Efficiency Estimates by Rolls Royce indicate that the maximum achievable core thermal efficiency is 60% [312]. Using the model developed for gas turbines, it is possible to provide a separate estimate the efficiency limit of the core. By assuming, a pressure ratio of 100 and ambient conditions at cruise, the Gas Turbine model yields a maximum technical limit of 62%.

Propulsive efficiency As the BPR increases, so does the size and drag of the nacelle.

Therefore BPR levels higher than 17.5 will not to be achievable because of the increased nacelle drag [313]. However, higher bypass ratios and hence propulsive efficiencies can be achieved with open rotor technology. Rolls Royce foresees that their open rotor technology under development is likely to achieve values of propulsive efficiency around 90% at 0.8 Mach [309]. On the other hand, in an article published by GE engineers the propulsive efficiency estimate for open rotors is 95% [314].

Transfer Efficiency An open rotor configuration would result in higher transfer efficiency because the losses incurred due to friction between the air flow and the nacelle would be reduced, as only one side of the flow would be in contact with the nacelle. However, no estimate of the transfer efficiency that would be achieved by an open rotor design was found in the literature. It is assumed that the limit lies between 90% and 95% considering that the open rotor design would halve the surface area in contact with the air flow thus halving the losses compared to today’s 85% transfer efficiency.

The assumption described above are used to estimate efficiency limit of jet engines. Table 4.3 includes a summary of the assumptions and their estimated variability.

Table 4.3 Summary of key parameter and efficiency limit for Jet engines, Device Current Efficiency Parameters Efficiency limit

TIT 1900-2100 K

CR 80-100

-Jet Engine 37-41 % η_c 92-93 % 54-58 %

η_t 93-95 % 10.6-9.9 g/kWs

η_{T R} 90-95 %

η_PR 90-95 %

Comparison with the literature

The upper bound of the overall efficiency estimate is in line with the theoretical efficiency limit defined by engineers at Rolls Royce which estimate a maximum thermal efficiency of 60% and a maximum propulsive efficiency of 95% [309]. On the other hand, other estimates found in the literature propose thermal efficiency between 50% and 55% which are only slightly lower than the thermal efficiency found in this study. The most likely reason for the discrepancy is that in other studies in the literature additional parameters such as noise and NO_xproduction are considered in the model