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Chapter2. Theory 5 For an enclosed control volume, Eq. 2.2 can be rewritten as follows [4]: F = c9 · (m ̇ 0 + m ̇ F − m ̇ B) − c0 · m ̇ 0 + A9 · (p9 − p0) (2.3) Here m ̇ 0 is the main mass flow, m ̇ F the fuel mass inflow, m ̇ B the bleed air offtake, A9 the nozzle surface area and p the pressure at in- and outlet respectively. Equa- tion 2.3 can be simplified further by neglecting the fuel and bleed mass flows, as they are comparably small to the main mass flow as well as assuming an adapted nozzle, so that the static pressure at the nozzle outlet is equal to atmospheric pressure, i.e. p9 = p0. This results in the simplified thrust equation 2.4 [4]. F = m ̇ 0 · (c9 − c0) (2.4) From Eq. 2.4 it can easily be deduced that thrust can be raised by either increasing the mass flow m ̇ 0 or the airspeed difference between inlet and outlet. This relates back to the definition of momentum in Eq. 2.1. The air passing through the jet engine is accelerated through a thermodynamic process chain by converting thermal energy into kinetic energy (jet) and mechan- ical work (fan). A jet engine is thus a heat engine. The thermodynamic cycle consists of compression, combustion and expansion stages and is known as the Brayton or Joule cycle. The ideal cycle is comprised of an isentropic compression in the compressor stages, an isobaric combustion in the combustion chamber and an isentropic expansion in the turbine stages of the engine. Work can be extracted from this cycle, because the isobars are diverging for increasing entropy. This means that the enthalpy difference of two pressures is bigger for larger entropies, i.e. in the turbine stages after combustion, where work is extracted from the cycle. Figure 2.1 depicts the ideal and real Brayton cycle. The ideal process is marked by isentropic datum points indexed Ps. The real cycle, marked in red, follows the same general thermodynamic procedure as the ideal one and is indicated by unindexed datum points P. The real processes are no longer isentropic or isobaric, however, resulting in pressure losses and entropy growth which in turn increase the enthalpy needed for compression and reduce the enthalpy that can be extracted from the cycle in the turbine stages. This is directly reflected in a decrease of thermal efficiency.PDF Image | Investigation of wing installation effects on the sound field of a model jet engine
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