6.1. LAMINAR-FLYING-WING DESIGN CONCEPT
reveals that the flow remains attached for both cases.
Figure 6.12: Spanwise lift distribution corresponding to a clockwise roll at take off with:
δa = +/−12.2◦ and δE =−2.5◦: M∞= 0.21 and CL= 0.61.
Table 6.3: LFW lift and drag coefficient breakdown.
Coefficient Cruise (suction) Cruise (no suction) Climb out
CL 0.14 0.38 0.61
CD 0.0023 0.01535 0.02721
CDi 0.00098 0.0072 0.01838
CDv,wing 0.00067 0.0075 0.0080
CDv,misc 0.00065 0.00065 0.00083
L/D 60.9 24.8 22.4
Table 6.4: LFW aerodynamic performance parameters for climb-out and takeoff with one engine inoperative, and cruise, with C.G. at 11.38 m.
Derivative Cruise (suction) Cruise (no suction) Climb out / Takeoff rotation
CL 0.14 0.38 0.61
M∞ 0.67 0.39 0.21
CLα (rad−1) 5.239 4.629 4.417
CLδE (rad−1) 0.834 0.762 0.742
Cmα (rad−1) 0.00115 -0.0100 -0.0163
CmδE (rad−1) -0.490 -0.433 -0.424
Cm,target 0.00056 0.0049 0.0161/0.146
α (deg) 1.5 4.8 8.3 / 11.3
δE (deg) -0.1 -0.8 -2.5 / -20.2
whilst extraction of the required suction power affects engine performance, and the associated hardware weight affects the structure and its weight.
In arriving at the aircraft design specification in Chap. 5, the optimum suction distribution for maintenance of laminar flow was combined with the aerofoil surface pressure distribution to obtain the optimum pump and viscous drag. However, for a detailed conceptual design study it is necessary to include the effects of a practical system architecture. The approach here is to take the basic arrangement proposed in Chap. 4 and apply it to the aircraft configuration shown in Fig. 6.8.
6.1.3.1 System Architecture
An illustration of the hardware arrangement for the centrebody region is detailed in Fig. 6.13.
Ideally, the spanwise chambers should be continuous across the span. This is made difficult by large variations in surface Cp associated with an increasing thickness-to-chord ratio (see Fig. 6.8), which would lead to violation of the incompressible flow assumption described in Chap. 4. By tailoring the chamber sets and corresponding pressures to each surface pressure distribution, high differential pressures are avoided. Therefore, the spanwise chamber arrangement is divided across three regions (with the dash-dot lines corresponding to changes in wing-section geometry). Flow rate controllers throttle the flow between chambers, which is then ducted into a set of chordwise ducts (each attached to a suction pump) located along the centrebody/outboard junction, and ejected at flight speed along the trailing edge of the centrebody. The grey areas correspond to regions where suction is not applied: over the leading edge suction is not required until some distance aft (see Chap. 4), whilst hardware space requirements and the presence of trailing-edge control surfaces limit its extent to the
6.1. LAMINAR-FLYING-WING DESIGN CONCEPT
first 90% of chord.
Duct entry
No suction regions
Pumps Spanwise chambers
y x
C1 C2
C3
C4
C5 B1
B2
B3
B4 A1
A2
A3
A4
Throttle valves
Chordwise duct
Chamber pressure:
point 1
Chamber pressure:
point 2
Chamber pressure:
point 3
Figure 6.13: Typical inboard suction-system architecture.
With no variation in wing section across the outboard and wingtip-fin regions, the ar-rangement consists of (separate) continuous chamber sets over each region. However, the sucked flow from the wingtip fins is throttled to match the chamber pressures of the out-board wings. The flow is subsequently transported to the collector ducts and pumps at the centrebody/outboard junction.
6.1.3.2 System Specification
The system architecture over each region is specified via the algorithm provided in Chap. 4.
However, ensuring that each region has a similar number of spanwise chambers introduces a further constraint on the ratio of non-dimensional pressure difference across the skin over
a single chamber width (erc). With reference to Fig. 6.13, an outline of the LFW system architecture specification algorithm is given below:
a) a boundary layer calculation at the inboard extreme of a region, where Rec is highest (leading to earlier transition prediction and suction initiation), sets the chamber layout and pressure, surface porosity distribution, and hence suction velocity distribution;
b) as Rec reduces outboards, for a constant distribution of skin porosity and chamber pressure, the associated level of distributed suction is insufficient to maintain laminar flow; therefore, the skin porosity coefficient,Ks, is increased uniformly across the region of interest until the suction level is sufficient at the outboard extreme of a region;
b) chamber depths are set such that inertial and frictional effects are small relative to the differential pressure across the skin, using Eq. 4.17;
c) the chamber pressures in region B are set higher than those in C, and those in A higher than in B, to attain the desired flow direction;
d) the ‘real’ suction distribution calculated over each region is combined with the chamber pressure distribution over region C, which sets the pump inlet pressures, to provide an estimate of the suction power.
For low values of Cl, it was shown in Chap. 4 that this parameter has a negligible effect on the suction requirements; therefore, spanwise variations in Cl across a region are neglected.
However, the highest values of Cl, shown in Fig. 6.9, over a spanwise region, are used to evaluate the suction requirements: these correspond to the surfaceCp distributions shown in Fig. 6.8.
Table 6.5 summarises the chamber properties for the inboard region. The maximum num-ber of chamnum-bers on the upper and lower surfaces is five and four, respectively; the minimum being two and four, respectively. Fewer chambers are required on the lower surface given the reasonably flat surface Cp distribution (see Fig. 6.8).
Table 6.5: Chamber specifications for the inboard section.
Parameter y <= 0.84 m y <= 4.20 m y <= 10 m
∆Pes,av 0.15 0.15 0.15
e
rc 4 4 6
k=Ks,actual/Ks,ideal 1.1 1.1 1.1
No. Chambers (upper / lower) 4 / 2 4 / 2 5 / 4
6.1. LAMINAR-FLYING-WING DESIGN CONCEPT
The distributions of surface pressure and chamber pressure (provided spanwise chamber losses are small) are detailed in Fig. 6.14 for region B (0.84 < y <= 4.20 m) and region C (4.20 < y <= 9.18 m). The solid line is the chamber pressure distribution across region B, and is determined based on consideration of the surface pressure distribution, indicated by the dash-dot line. Region B has one small chamber upstream of the suction peak, and three downstream. The chamber pressures in region C are lower than those over region B, and hence ensure the desired flow direction. (Note, that the last chamber of region C is isolated and not connected to region B.)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2
x/c
!P
Surface: y = 4.20 m Chamber: y = 4.20 m Chamber: y = 9.18 m
Figure 6.14: Distribution of inboard chamber and surface (non-dimensional) pressures across regions B and C.
The critical differential pressures, corresponding to a flow Mach number of 0.4 across the porous skin, for the three regions considered are detailed in Fig. 6.15. The maximum
∆Pes across the skin is below critical, and therefore the assumption of incompressible flow is satisfactory. A maximum chamber depth of around 3 cm is required to keep chamber pressure losses small.
The chamber specifications for the outboard and wingtip fin regions are summarised in Tab. 6.6. The sharp trailing-edge constraint results in a steep pressure gradient over the rear of the outboard aerofoil, leading to a greater number of spanwise chambers relative to the inboard regions. However, relative to the outboard region, fewer chambers are required over