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Master Thesis Report Literature Review Substituting the expression for the inlet recovery ratio into the exit velocity: 2 V2 = ρFPR∗ The total thrust produced can then be expressed as follows: ∗PT0 −Ps,2 (2.18) (2.19) (2.20) Defining the mass flow as: loss 2 T=m ̇∗( ρFPR∗ ∗PT0−Ps−V0) loss m ̇ = ρApV1 = ρπDp2V1 4 The total thrust produced can finally be expressed as follows: ρπDp2V1 2 T= 4 ∗( ρFPR∗ Considering that the total thrust produced has to be constant in steady and level flight, the following relation can be observed: • As the inlet recovery ratio decreases, the fan diameter has to increase in order to produce the same thrust. This implies an increase in the structural mass of the propulsion system. • As the inlet recovery ratio decreases, the exit velocity also reduces which implies a reduction in the specific thrust. From this relation, it can be said that an embedded propulsion system with lower pressure recovery tends to suffer from a lower specific thrust and therefore require a larger fan diameter to achieve the same level of thrust. As such, more horsepower is required in order to drive the same fan pressure ratio with greater airflow. This additional power has to come from a larger core airflow and hence increased fuel flow for the same combustor exit temperature. Therefore, the result of a reduced inlet recovery ratio is a larger core to power the propulsion system. Boundary layer ingestion also has an influence on both the thermal and propulsive efficiency. The propulsive efficiency is related to the level of wasted kinetic energy trailed by the wake of the propulsion system. It is a measure of how effective the net work output is converted to thrust power. ∗PT0 −Ps,2−V0) (2.21) ηp = PropulsivePower RateofProd.ofPropulsiveKE Substituting equation 2.13 into equation 2.22, ηp = m ̇ (Vj − V∞)V∞ 12m ̇(Vj −V∞)(Vj +V∞) = TV∞ 12m ̇ (Vj2 − V∞2 ) = 2 1+ Vj (2.22) (2.23) Substituting the expression for the exit velocity, the propulsive efficiency can then be expressed as follows: 1+ Vj 2FPR∗ ∗PT −Ps,2 V∞1+ρ loss0 V∞ loss 22 ηp= = (2.24) V∞ 10PDF Image | Aerodynamic Design of the NASA Rotor 67 for Non Uniform Inflow
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