Design Point Sizing

Similar to a conventional propulsion system, the size of a propulsor is determined by the propul-sive force required. The required mass flow for a free-stream propulsion system can be rea-sonably simply obtained as performance is independent from its size. However, in the case of a BLI system, changes to the propulsor and inlet dimensions will influence the averaged flow characteristics at the interface point by changing h/δ. Estimation of the size of a BLI propulsor using the method developed in this research therefore necessitates a procedure to solve for the propulsor size that produces the required net propulsive force (Figure 3.6 and Appendix B):

1. Establish the local flow characteristics:

• Reynolds number, Re

• Boundary Layer thickness, δ

• Local free-stream velocity, u0i

2. Determine the boundary layer flow characteristics:

• Mass flow, ˙mBL, Equation 3.8

• Average total pressure deficit, ¯P_BL/P₀, Equation 3.12

• Average velocity, ¯u_BL/u0i, Equation 3.14 3. Guess streamtube height, h, and hence obtain h/δ 4. Determine streamtube flow characteristics:

• Mass flow, ˙m_i, Equation 3.23

• Average total pressure deficit, ¯Pi/P0, Equation 3.28

• Average velocity, ¯u_i/u_0i, Equation 3.29 5. Estimate installation terms:

• Skin friction drag of surface from station i to intake highlight, τ_w,iS_wet,i

• Nacelle drag, D_nac

• Drag of airframe wetted surface area covered by propulsion system control volume, (S_wet,iand wL_nacelle) , ∆D

Propulsor

Figure 3.6: BLI propulsor simulation method at design point

6. Estimate propulsion system performance and check net propulsive force, NPF (Figure 3.7 for a propulsor consisting of intake fan and nozzle)

7. Return to Step 3 until target net propulsive force is met

This procedure is a generic workflow that can be applied to any propulsion system configura-tion or architecture. In order to simplify the analysis, it is assumed that the thickness of the boundary layer does not vary significantly over the width of the inlet streamtube. In addition, a square streamtube cross-section has been assumed throughout. However, this assumption may break down depending on the configuration of the aircraft and propulsion system. Unlike 2- or 3D methods, additional inlet pressure loss due to the boundary layer and compressor efficiency loss due to distortion are not directly represented. These are instead introduced into performance calculations of Step 6 as averaged numerical approximations. For the purposes of this research, the specific heat coefficient for air as a function of temperature was determined using ESDU 00.01.08 data. Gross and net thrust calculations follow AGARD 237 [98]. The gross thrust is scaled by a C_v, the ratio of actual specific thrust to the ideal specific thrust.

Whilst boundary layer flow characteristics may be assumed to be fixed for a fixed flight con-dition, they will be dependent on the propulsor location. A propulsor located at the trailing edge of a fuselage will ingest a significantly thicker boundary layer than a propulsor located near the leading edge. The local velocity of the free-stream flow entering a propulsor will also de-pend on the aircraft configuration due to the velocity profile over the fuselage. For blended wing body type configurations, the aerofoil cross-section leads to a flow acceleration and subsequent deceleration from the leading to trailing edges. Non-lifting fuselages such as the fuselage of a tube-and-wing will experience a deceleration of flow due to the skin friction (leading to the aircraft wake). Propulsion system performance therefore cannot be determined entirely inde-pendently from the aircraft and will rely on an estimate of the aircraft configuration. Location and configuration factors will play a significant effect on the performance of a propulsor. Each propulsor should be individually sized for the best performance given its location [105]. Deter-mining the local flow characteristics is therefore the first step in sizing the propulsion system, shown in Step 1 of the above process. The most favourable location can then be selected as a part of the sizing and design process.

The method in Figure 3.7 presents the relationship for performance of a propulsor with critical exhaust flow. It is possible that the nozzle pressure ratio will not be equal to the critical value, and that the exhaust flow will therefore be slightly under or over-expanded. However, for the low pressure ratios considered in this research the exhaust is close to fully expanded.

Performance calculations for fully expanded flow were therefore assumed to be applicable for the purposes of this research.

Nacelle drag estimation is an additional factor for the integrated engine performance and the NPF model. For the purposes of this research a simple nacelle design was implemented for nacelle drag estimation. This included a NACA-1 forebody and a circular arc afterbody. An overview of the sizing process is shown in Figure 3.8 including the assumptions made for the

3. Propulsion System Modelling

Figure3.7:Propulsorperformanceflowchart

Figure3.8:Nacellesizingflowcharttoprovideanestimateofnacelledimensions,NACA-1forebodyandcirculararcafterbody,withassumptions

3. Propulsion System Modelling

Figure 3.9: Definition of key intake areas

sizing process. Due to the integrated configuration, the lower surface of a BLI system is em-bedded in the airframe. The nacelle drag for a BLI propulsor is therefore estimated assuming that the nacelle consists only of the upper nacelle surface with wetted surface area approxi-mately equal to the nacelle length, L_nacelle multiplied by the propulsor intake width, w. The two propulsor at the extreme edges of the array have an additional nacelle component due to the end wall with a wetted surface area approximately equal to L_nacelle multiplied by the highlight height.

A number of key areas can be used to define the size of the intake and the propulsors (Figure 3.9). The intake throat, highlight, and fan face areas may be sized by defining fixed Mach numbers for the throat and fan face and a contraction ratio between the throat and the highlight. The propulsor sizing process produces the area of the incoming streamtube, A_i. The area of each section of the intake may then estimated by using the area ratio A/A^∗. Mach number at station i is assumed to equal the mass flow average Mach number for the incoming streamtube. In order to ensure that the throat will not be choked or close to choking, a throat Mach number of less than one should be selected. A contraction ratio, CR, must also be selected between the throat and the highlight. The mass flow ratio of the propulsors at design point is therefore less than one, as the highlight area, A_H, is greater than the area of the streamtube at station i. Intake areas relative to the streamtube area at station i may be obtained using the area ratio for isentropic flow:

A A_i = Mi

M

1 +^γ−1₂ M² 1 +^γ−1₂ M_i²

!_2(γ−1)^γ+1

(3.31)

Subsequently, the highlight area, A_H can be obtained given an assumed contraction ratio from the throat area A_th.

AH = CR × A_th (3.32)

The fan area, A_{f f}, resulting from the selected fan face Mach number may be used to estimate the fan diameter by including an assumed hub-to-tip ratio, λ_fan:

Dfan = 2

s A_{f f}

π(1 − λ²_fan) (3.33)