3. Propulsion System Modelling
3.1.6 Off-Design Extension
A key aspect of developing a new model for simulating a boundary layer ingesting propulsion system was to enable the use of the model over the full aircraft mission profile. The reviewed literature presented at the beginning of the chapter does not provide a method for simulating BLI propulsion systems at off-design. Therefore, this section will detail the extension of the design point method detailed in the previous sections for use at off-design and hence any altitude, Mach number, or propulsion system power setting.
Figure 3.10: Generic scaled fan/compressor map with peak efficiency running line
The performance of a propulsion system at off-design can be represented by maps that relate pressure ratio, mass flow, rotational speed and/or efficiency of each propulsion system component. At off-design, the change in mass flow demanded by a propulsor may be rep-resented by the selected component running lines. This depends on the configuration of the components, such as nozzle area, or variable subcomponents such as inlet guide vanes. The mass flow demand may be presented as a non-dimensional mass flow (NDMF) that is indepen-dent from the flight conditions:
NDMF = m˙√ T
P (3.34)
The running line of the component provides a relationship between the mass flow through the component, its pressure ratio, rotational speed, and efficiency (Figure 3.10). The selected component maps will dictate the performance of a component. The mass flow demanded by the operating point of each component must be matched to the operating point of other components within the propulsion system. The nozzle area is a dominant factor in determining the overall operating point of the propulsion system. Assuming a fixed nozzle area, the non-dimensional mass flow of upstream components is dictated by the non-dimensional mass flow of the nozzle.
For example, the non-dimensional mass flow of a choked nozzle is constant. This then provides a point to which the operating point of upstream components must be matched. A floating nozzle area will remove the nozzle as a factor that dictates performance of the propulsion system. In particular, research on the N3-X identified a variable area fan nozzle as a necessary requirement to ensure fan stability at the low pressure ratios considered for a BLI propulsor [24, 56].
The size of the inlet stream varies depending on the mass flow demand, with a high mass flow demand resulting in a larger cross-sectional area for the incoming streamtube of air. This can be linked to the capture area ratio (CAR) term: the ratio of inlet area to the streamtube area. The capture area ratio of a propulsion system may be defined as follows:
CAR = Ai
AH (3.35)
For an engine operating in free-stream flow, the mass flow can be obtained from the dimensional mass flow without estimating the streamtube size. The total pressure term in
non-3. Propulsion System Modelling
dimensional mass flow and the velocity of the capture streamtube are functions of the flight velocity and altitude. For a BLI system, the size of the streamtube will have a noticeable effect on the characteristics of the flow entering the intake. An engine operating with a high capture area ratio will ingest predominantly free-stream air, with a very high ratio of h/δ. In contrast, a propulsor operating with a low capture area ratio may ingest predominantly boundary layer. The boundary layer thickness is also a function of the flight velocity, amongst other factors. A slow-moving or static aircraft will have a negligible boundary layer thickness. A propulsor operating at sea-level static conditions may therefore perform very similarly to a conventional free-stream propulsor. The flow characteristics required for the non-dimensional mass flow are therefore a function of the size of the inlet streamtube and hence the capture area ratio or mass flow demand. This is particularly apparent for the total pressure term, as the (mass flow-averaged) total pressure deficit resulting from the boundary layer is a function of the boundary layer flow characteristics and the ratio h/δ (Equation 3.28). For example, the pressure term at the fan face can be determined as a function of h/δ:
P2 = ηinlet
Where ηinlet is the total pressure loss through the inlet and P2 is a function of h/δ through Pi. Depending on the configuration, an additional term may be required to determine the total pressure loss due to separation of the incoming flow at the lip or of the boundary layer. Note that it has been assumed that the flow is isentropic and that there is therefore no loss in total temperature:
T2= T0
t t (3.38)
Given the definition of station i, the boundary layer flow characteristics are determined by the Mach number and altitude, regardless of the propulsion system power setting. These may therefore be calculated independently from the streamtube flow characteristics, without know-ing the value of h/δ that matches mass flow demand to the streamtube mass flow. Given this relationship between flow characteristics and the size of the inlet stream, a mass flow-matching procedure is required to match the upstream mass flow and streamtube size to the mass flow demanded by the propulsor. The procedure follows a similar flow to the design point sizing and performance process, except the goal is now to match mass flow rather than meet a target thrust. For a known operating point, the procedure to obtain performance of a BLI propulsor at off-design is as follows (Figure 3.11):
1. Obtain the propulsor and component operating speed line (follow standard procedures for mass flow matching of conventional propulsion system components)
2. Obtain the fan non-dimensional mass flow, NDMF, at the given operating point 3. Determine the boundary layer flow characteristics:
• Mass flow, ˙mBL, Equation 3.8
• Average total pressure deficit, ¯PBL/P0, Equation 3.12
• Average velocity, ¯uBL/u0i, Equation 3.14 4. Guess streamtube height, h, and hence obtain h/δ
Propulsor
Figure 3.11: BLI propulsor simulation method at off-design
5. Determine streamtube flow characteristics:
• Mass flow, ˙mi, Equation 3.23
• Average total pressure deficit, ¯Pi/P0, Equation 3.28
• Average velocity, ¯ui/u0i, Equation 3.29
6. Estimate total pressure and temperature at the fan face, Equations 3.37 and 3.38 7. Calculate mass flow at the fan face from the mass flow demand, NDMF, Equation 3.34 8. Return to Step 4 until streamtube mass flow in Step 5 matches the propulsion system
mass flow demand in Step 7
9. Estimate propulsion system performance using streamtube flow characteristics from Step 5 and the engine component operating points (Figure 3.7 for a propulsor consisting of intake fan and nozzle)
The mass flow matching method is a generic workflow that is intended to be applicable for any propulsion system configuration. This procedure should be included within the matching process for the component operating points to determine the engine’s overall operating point.
The non-dimensional mass flow for each component is a function of the engine’s operating point. Iterative loops may therefore also be required to find the point where the component operating points are matched and h/δ matches the resulting mass flow demand. Once the engine’s operating point has been determined and the mass flow matching procedure is com-plete, the performance of the propulsion system may be estimated by following conventional 1D gas dynamics methods, as with the design point method. The goal of the above process is to determine inlet flow characteristics, given that the capture area ratio and hence h/δ is initially unknown.
A number of additional general assumptions are applied consistent with the assumptions used for the design point method:
• Flow at interface point is independent of propulsor demand
• Constant ratio of free stream to boundary layer air, h/δ , from the interface point onwards
• Streamtube flow characteristics are averaged from the interface point onwards
• Square streamtube cross-section of constant width
• Each propulsor in an array operates independently, streamtubes are unconstrained by adjacent fans
Given the constant width cross-section assumption, the capture area ratio of the propulsor may be defined as follows:
CAR = Ai
AH = h
hH (3.39)
3. Propulsion System Modelling