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Master Thesis Report Literature Review Figure 2.4: Podded versus Embedded Engine Concept [1] then used as the inlet velocity into the engine. The propulsive force provided by the engine balances the momentum deficit caused by the airframe drag: Fengine = m ̇ (Uj − Uw) = m ̇ (U∞ − Uw) = DA (2.3) The mechanical power required to produce this force in the presence of boundary layer ingestion is then formulated as such: PBLI = m ̇ (Uj2 −Uw2) = m ̇ (Uj −Uw)(Uj +Uw) = Fengine(Uw +U∞) (2.4) 222 Comparing equation 2.2 and 2.4, it can be seen that the embedded engine concept with BLI requires lesser mechanical power since Uw < Uj. Power Balance Method Another way of investigating the benefit of boundary layer ingestion is to use the power balance method developed by Drela [2]. This method is based on the conservation of total power. The rate of energy entering into the system equates the rate of energy leaving the system. Specifically, the sum of the total mechanical power supply is equal to the sum of the total viscous dissipation rate, Φtotal and the mechanical energy flow rate out of the control volume (CV), ε ̇. The total mechanical power supply is made up of three terms; the net propulsor shaft power Ps, the net pressure volume power, Pv power and the net propulsor mechanical energy flow rate into the CV, Pk. Mathematically, the power balance equation can be expressed as follows: Ps +Pv +Pk =ε ̇+Φtotal (2.5) The first term on the R.H.S represents the energy flow out of the control volume while the second term represents the energy loss within the control volume. The mechanical energy outflow rate, ε ̇ can be decomposed into 5 main terms; the potential energy rate, W h ̇ , the wake streamwise kinetic energy deposition rate, E ̇a, the wake transverse kinetic energy deposition rate, E ̇v, the wake pressure defect work rate, E ̇p and the wave pressure work and kinetic outflow rate, E ̇w. Taken all these together, the power balance equation can be expressed as follows: Ps +Pv +Pk =Wh ̇ +E ̇a +E ̇v +E ̇p +E ̇w +Φtotal (2.6) 6PDF Image | Aerodynamic Design of the NASA Rotor 67 for Non Uniform Inflow
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