2.1 Flow physics

In 1904, Prandtl [Reference Tollmien, Schlichting, Görtler and Riegels25] conceptualised that the flow over a body has a thin region attached to the surface called boundary layer, where the viscous effects are dominating. The flow near the surface is brought to rest, developing a velocity gradient until the edge of the boundary layer, where the flow is inviscid. The turbulent boundary layer has steeper velocity gradients near the wall, resulting in higher skin friction drag. The increased boundary layer thickness also increases the displacement of the external flow, resulting in a marginal increase in pressure drag. Re $_{{\rm{i}}nd}$ is defined by Schlichting [Reference Schlichting and Gersten26] as the minimum Reynolds number below which instability does not rise. The developing boundary layer is subjected to external disturbances due to receptivity and initiates the transition process [Reference Morkovin27] as they excite disturbance waves. These disturbance waves superimpose the laminar base flow and become unstable at R $_{{\rm{i}}nd}$ . The amplification of these disturbance waves in the primary instability mechanism can be theoretically modelled by linear stability theory. ${e_N}$ method [Reference Van Ingen28, Reference Smith29] is a semi-empirical approach using linear stability theory to analyse the stability of a laminar boundary layer by superimposing harmonic oscillations as small disturbances on an otherwise steady flow. The amplification of these disturbances downstream at a station x is denoted by an amplification factor, called N factor as defined as

\begin{align*}N = ln\frac{a}{{{a_o}}} = \int_{{x_o}}^x {a_i}dx \end{align*}

where ${x_o}$ is the station where the disturbance with frequency $\omega $ and amplitude ${a_o}$ first becomes unstable. The method uses a database of the frequency response of the instabilities linked to the state of the boundary layer. It does not model the physics of the boundary layer transition. However, as the growth of disturbances from $N = 0$ to $N = 7$ is linear, a large part of the amplification dominated by Tollmien – Schlichting instabilities (TSI) is predicted very well by the ${e_N}$ method. Extrapolation to the non-linear interactions of the disturbance, is only necessary for a short region ( $N \gt 7$ ) of the N factor growth curve due to its exponential nature. Flow is predicted to transition to turbulent flow when the N factor reaches a critical value called ${N_{{\rm{c}}rit}}$ .

Figure 1.

Critical N Factor and Effect of BLS on TSI

The value of ${N_{{\rm{c}}rit}}$ is experimentally validated and differs with receptivity factors. ${N_{{\rm{c}}rit}}$ value of 13 is used in this study for flight conditions based on the in-flight experiments conducted with DLR flying testbed ATTAS (Advanced Technologies Testing Aircraft System) [Reference Redeker, Horstmann, Koester, Thiede and Szodruch30, Reference Horstmann, Redeker, Quast, Dressler and Bieler31]. N-factor identification was performed using a specially designed wing glove with modified sections. Linear stability analysis delivered amplification rates for cross-flow instabilities (CFI) and TSI. The measured transition locations from the same experiment were used to correlate the envelopes of ${N_{{\rm{T}}S}}$ and ${N_{{\rm{C}}F}}$ , as shown in Fig. 1(a). The exact values of ${N_{{\rm{c}}rit}}$ is then taking into account the desired transition location for the range of application of the present research, in particular same value has been chosen for parallel studies inside the SE²A Cluster that can be found in [Reference Beck and Landa18, Reference Sudhi, Elham and Badrya24].

2.2 Aerodynamic solver and transition prediction

Flow transitions from laminar to turbulent flow due to the amplification of instabilities. Three sources of instabilities occur on the wing during flight: (1) Tollmien – Schlichting instabilities (TSI), (2) cross-flow instabilities (CFI), and (3) attachment line instabilities (ALI). Boundary layer suction is an approach towards dampening the growth of these instabilities. The transition to turbulent flow is delayed by removing a small portion of the boundary layer near the wall as shown in Fig. 2. This suction also helps to maintain a stable shape factor for the velocity profile and delays separation. By introducing wall-normal velocity to the Prandtl boundary layer equation, suction velocities necessary to laminarise a flow are derived. For a flat plate, the non-dimensionalised suction velocity is given by [Reference van de Wal17]

(1) \begin{align}\frac{{{v_o}}}{{{U_\infty }}} = \frac{1}{{0.2205}}\frac{1}{{\dfrac{U}{{{U_\infty }}}}}\frac{{d\left(\dfrac{U}{{{U_\infty }}}\right)R{e_\theta }}}{{d\left(\dfrac{x}{c}\right)R{e_c}}} \end{align}

Figure 2.

Schematic representation of boundary layer suction [Reference Boermans32].

A modified solver based on XFOIL [Reference Drela33] with the integration of a full ${e_N}$ method called XFOILSUC [Reference Bongers34, Reference Ferreira35, Reference Broers36] is used for the aerofoil design. XFOILSUC is a panel-based code that is well suited for the design and analysis of subsonic aerofoils and is computationally inexpensive for performing design optimisation compared to high-fidelity CFD solvers. The original ${e_N}$ envelope method used for transition prediction in XFOIL predicts the N factor growth based on a linear approximation of the envelopes of the spatial amplification curves and was derived for self-similar Falkner-Skan laminar boundary velocity profiles [Reference Drela33]. This approach, however, cannot predict the damping of T-S waves due to BLS. XFOILSUC has an improved transition prediction capability coupled to the integral boundary layer solver along with a suction boundary condition. A new database full ${e_N}$ transition prediction method called improved Van Ingen method (IVI) [Reference Van Ingen37, Reference Van Ingen38] is used in XFOILSUC. IVI method can predict N factor damping due to BLS, as seen in Fig. 1(b). This method can track the amplification and damping of 601 frequencies logarithmically spaced values between 10 $^{ - 7}$ and 10 $^{ - 1}$ , based on the stability data from Arnal datasets [Reference Arnal39]. Inside the SE²A Cluster, a series of 2D optimisations are performed to deisgn the aerofoil able to maintain a low drag with a low power suction absorption for boundary layer suction. These optimisations were done for different Cl and onset of suction and resulted in the SE²A HLFC aerofoil. One of the optimisations useful for the HLFC aerofoil was set for Cl = 0.4, Re = 16 M, $M = 0.4$ with no limits of the extension of the laminar flow. Accuracy of XFOILSUC in predicting the flow and transition behaviour is compared with the Reynolds Averaged Navier Stokes solver TAU in Fig. 3.

Figure 3.

Comparison between XFOILSUC and TAU [Reference Sudhi, Elham and Badrya24].

The shape factor and friction coefficient are in good agreement, especially until 80% of the chord. However, TAU predicts a transition at 83% while for XFOILSUC transition happens at 85% of the chord. The N factor amplification predicted by XFOILSUC shows similar behaviour as the envelope of instability amplifications calculated by linear stability theory (LST) using the boundary-layer code COCO-LILO [Reference Schrauf40]. XFOILSUC is based on the Arnal stability diagrams while LILO uses non-local linear stability analysis by solving the Orr-Sommerfeld equation. It is solved thanks to boundary layer profiles calculated by COCO for a range of frequencies. The possible difference given by XFOILSUC in the estimation of transition and hence drag respect to higher fidelity tools, is considered as acceptable, in particular considering the interest in studying the possible changes in the transition line with the use of suction. A solution to avoid the possibility of calculation of transition and aerodynamic parameters over a separation bubble that may lead to inaccuracies is to use a forced transition. In this research, optimised results are aerodynamically tested for forced transition at 80% chord, and they show a limited drag difference keeping the optimised results for free transition more conservative and fundamental to understand the shifting of the transition point.

Figure 4.

Aircraft sizing procedure from PyInit within SUAVE.

4.1 Definition of the problem and design variables

The application of BLS drastically changes the friction drag of a wing. Therefore, the optimal geometry of the wing will be influenced by this technology. Besides, since the total value of the aerodynamic drag is reduced, the balance between the aerodynamic drag and structural weight of the wing is influenced, so a new optimal point is expected as the compromise between drag and weight. In this section, an aircraft wing MDO is presented to investigate the influence of the BLS on wing design. To achieve this goal, physics-based methods for aerodynamic analysis and structural weight estimation are implemented.

For the full electric aircraft, the aircraft maximum take-off weight (MTOW) is used as the objective function. The root and tip aerofoil shapes are fixed. The maximum thickness to chord ratio at the two different positions is scaled and used as design variables. Besides, geometric parameters like span, sweep angle with respect to the leading edge, chord root and taper ratio complete the design vector. Two different configurations are analyzed, the first equipped with the NACA 65(2)415 aerofoil and the second with the HLFC SE²A aerofoil. Design variables are shown in Table 3.

Table 3.

Design reference variables and boundaries

A gradient-free optimisation algorithm is used. In fact, XFOILSUC does not compute derivatives and the use of a finite difference method to build the gradient is discouraged. In fact, the tool can be characterised by convergence issues not producing feasible results. The solution commonly applied for this occurrence is the computation of parameters, like drag, for a region of lift coefficients at the boundary of the initial value, which is not giving a proper numerical solution. Thanks to the generation of this polar for the corresponding aerofoil, the researched value of the selected point can be picked. Otherwise, a possible less computational solution is the use of an interpolation scheme along the span, if few values are not obtained. In case of the failure of all these strategies, or if the number of not converging sections is too high, the design vector is neglected and for a free-gradient optimisation the algorithm can keep searching. Hence for the possibilities of this discrete domain, the correct computation of a gradient and so of a direction is difficult. Finally, gradient-based optimisations suffer from the possibilities of convergence at local minima. In particular, the Genetic Algorithm toolbox of Matlab was chosen for optimisation. The initial population matrix consist of a Latin Hypercube sample matrix in Matlab of 30 individuals, obtained considering as upper and lower boundaries the same boundaries of the optimisation process: a variation of 25% from the reference design vector. The taper ratio has been limited to 0.252 as a minimum due to the non-feasible acceptance of lower values. However, it represents a further reduction percentage with respect to other parameters thanks to promising preliminary results with values close to 0.3. The first vector of the matrix is represented by the reference vector itself used as a first-step check of the study, expecting a fitness value equal to the unity. A total of 100 generations are evaluated for optimisation, which is performed for the cruise configuration. However, the wing shape optimisation may result in unrealistic values of the design variables because the value of wing loading is affected by some other segments of flight like take-off, climb, landing [Reference Mariens, Elham and van Tooren47]. In fact, the design of real wings should also consider requirements as aircraft stability, control characteristics, and aeroelastic effects in high speed [Reference Mariens, Elham and van Tooren48]. The current MDO is focused on the new integration between the Q3D solver and XFOILSUC for the boundary layer suction and, hence, not all of the mentioned constraints are applied. Considering the current cases (low speed, regional electric aircraft), the take-off, landing, and climb performance are considered by keeping the wing loading smaller or equal to that of the reference aircraft.

(2) \begin{align}\left( {\frac{{{W_{TO}}}}{S}} \right) \le {\left( {\frac{{{W_{TO}}}}{S}} \right)_{reference}} \end{align}

This requirement is not given by a constraint function but the fulfillment lies in the use of the Heaviside function for the fitness evaluation. In particular, the fitness function is expressed as:

(3) \begin{align}J = \frac{{{W_w} + {W_b} + {W_{rest}}}}{{{W_{T{O_{reference}}}}}} + Heaviside(err - 0.1) \end{align}

While the wing loading evaluation is exhibited as an error function:

(4) \begin{align}err = \frac{{\dfrac{{{W_{TO}}}}{S} - {{\left( {\dfrac{{{W_{TO}}}}{S}} \right)}_{ref}}}}{{{{\left( {\dfrac{{{W_{TO}}}}{S}} \right)}_{ref}}}}\,\% \end{align}

Recalling the properties of the Heaviside function, in case the wing loading is higher than the reference one at least of a quantity higher than 0.1%, the function of a value higher than one will have one as output. In this case, $J \gt 1$ , so the wing loading requirement is pursued through the optimisation process. The tolerance of 0.1% is needed because if the two-wing loading were equal, the Heaviside function would produce a $0.5$ value. Finally, error values until $0.1\% $ are considered acceptable for the whole optimisation framework. The second demand dealt in the present research wants to guarantee the performance requirements for the climb, in particular for the climb gradient considering the second climb segment with one engine inoperative [Reference Torenbeek44]. The request is satisfied for an aspect ratio (AR) larger than typical values of turbofan passenger aircraft categories [Reference Raymer42, Reference Jenkinson, Rhodes and Simpkin49], in particular:

(5) \begin{align}AR \ge 8 \end{align}

In this work, the reference aspect ratio is 16, considering as target the minimisation of ${W_{TO}}$ reducing the overall drag, for the characterisation of the problem AR is, of course, kept higher than the value in (5) without the use of any constraint function, in this way computational time is substantially lowered. The scheme chosen for mutation is the ‘mutation adapt feasible’, considered as necessary in case of bounds or linear constraints. It randomly generates directions that are adaptive with respect to the last successful or unsuccessful generation. The mutation chooses a direction and a step length that satisfies bounds and linear constraints. A default crossover fraction of 0.8 is used. The convergence history for both optimisations can be seen in Fig. 7.

Figure 7.

Convergence history.

The optimisation algorithm can be graphically represented using the extended design structure matrix, XDSM [Reference Lambe and Martins50] in Fig. 8.

Figure 8.

XDSM for wing optimisation.

Figure 9.

Forces and angles according to sweep theory [Reference Mariens, Elham and van Tooren48].

4.2 Wing aerodynamic analysis

The wing’s aerodynamic analysis was performed using a quasi-three-dimensional (Q3D) method [Reference Mariens, Elham and van Tooren48]. In the Q3D approach, the total drag of a wing is decomposed into three components: induced drag, pressure drag and friction drag. The sum of pressure and friction drag is defined as profile drag. The induced drag is the drag caused by the tilting of the lift vector due to downwash angle variation done by tip vortexes.

The overall procedure of the proposed method is broken down into the following stages, as shown in Fig. 10. At first, wing geometry is divided into several two-dimensional (2D) spanwise wing sections. The AVL [Reference Drela and Youungren51] software based on the Vortex Lattice Method (VLM) is used to calculate the wing lift distribution, the wing lift coefficient ${C_L}$ and the wing induced drag coefficient ${C_{Di}}$ . ${C_{Di}}$ is calculated using Trefftz plane analysis [Reference Meheut and Bailly52]. The lift coefficient is interpolated to find ${C_l}$ at a given spanwise section. Sweep theory is applied to obtain ${C_l}$ , Mach number and velocity, normal to the sweep line Fig. 9. The effective velocity and Reynolds are then evaluated and become the input of XFOILSUC to compute the effective angle-of-attack and effective drag parameters using strip theory [Reference Flandro and McMahon53]. Steps are repeated in an iterative process until the induced angle-of-attack is converged, as can be seen in Fig. 11. Finally, the profile drag coefficient is obtained in the streamwise direction. The wing total profile drag is calculated by integrating the parasite drag coefficient of the 2D sections over the span, and from its sum with the induced drag, wing total drag is obtained.

Figure 10.

Detailed steps for the ${C_d}$ profile evaluation.

Figure 11.

Induced angle-of-attack convergence.

4.3 Wing weight estimation

The aircraft wing weight is estimated using the EMWET tool [Reference Elham, La Rocca and van Tooren54]. EMWET is a physics-based structural sizing and weight estimation tool. In EMWET, the wing structural weight is based on two contributions: primary and secondary structure. The primary structure group is further decomposed into the so-called optimum and non-optimum structure weight contributions. The former contributions include the spar webs and the upper and lower equivalent panels of the wing box, whose weight is determined analytically, evaluating the amount of material required to carry the critical loads. The latter contributions include weight penalty items such as joints, attachments, cutouts, etc. These, together with the secondary weight contributions, such as fixed leading and trailing edges, high lift devices, and movables, are determined using empirical methods [Reference Elham, La Rocca and van Tooren54]. Since EMWET is developed for conventional wings and is calibrated using conventional transport aircraft with metal structures, the final wing weight is ‘corrected’ with a coefficient that so reduces the total wing weight computed before, in particular, the effects of structure layout and novel materials are assumed to reduce the empty weight by 15% compared to the metal structure.

To calculate the primary structure weight in EMWET, the aerodynamic loads applied to the wing are required. The loads are calculated using the Q3D aerodynamic solver for critical load conditions, considering the load alleviation technology. The wing box is shown in Fig. 12(a). The skin, the stringers and the spars caps are modelled using just one upper and one lower equivalent panel. The webs of the front and rear spars are modelled separately using simple vertical panels. The upper and lower panels are sized to withstand the bending moments, whereas the spar webs are sized based on shear loads. The front and rear spars are located at 20% and 70% of the local chord. Considering that the wing characteristics, like the aerofoil thickness, are changing during the optimisation, the transition point is also changing (Fig. 12(b)). Therefore, the starting point of boundary layer suction can change during the optimisation. However, the end of suction is fixed at the rear spar position due to structural issues and gives the boundary layer time to transit to a turbulent one before it reaches movable surfaces.

Figure 12.

Wing modeling for weight estimation and BLS.

6.1 Design vectors and geometry

Optimised design vectors are summarised in Table 4, for two different optimisations, one with the NACA 65(2)415 and one with HLFC $S{E^2}A$ aerofoil. Results are showed in Table 4. From Table 5 it can be noticed that the best performance is reached with $S{E^2}A$ aerofoil geometry optimisation. The MTOW is reduced by 6.09%, while the total drag coefficient of the aircraft is decremented by 22.27%.

Table 5.

Optimisation results

Aerofoil data in Table 4 can be plotted in Fig. 14 while the wing geometry is represented in Fig. 15.

Figure 14.

Comparison of NACA 65(2)415 and $S{E^2}A$ aerofoil at root and tip, respect the reference one.

Figure 15.

Wing geometry comparison.

The optimisation results in a scaled aerofoil with an increment of thickness and mainly an increment of the aspect-ratio of the wing. The optimiser, considering the possibility of scaling the aerofoil without changing the shape (considering the limited design variables to keep low computational time), is trying to augment the thickness of the aerofoil so as to reduce the bending loads and as a consequence, EMWET is computing a lighter wing. Besides, a higher thickness may favour more natural laminar flow in the upper surface and lower power absorption, saving part of the battery mass. Drag is essentially reduced acting on the profile drag by the active flow control and increasing the span to reduce induced drag. The potential augmentation of the surface is compensated by the aerodynamics benefits. In Fig. 16 is shown the ‘snowball effect’ [Reference Elham56] for the reduction of the MTOW. In fact, the reduction of drag brings to a lower thrust request and power absorbed by the BLS system and hence a reduced battery weight. These elements and a lower wing weight make the MTOW being reduced and from this a lower lift that again favours a reduction of the drag. Nevertheless, optimisations could be also not characterised by an increment of thickness. For example, the possibility of changing the shape of the aerofoil as a design variable, the use of fixed transition or the onset of suction, may lead to a different solution from the optimiser.

Figure 16.

Snowball effect for weight reduction.

6.2 Aerodynamic and structural results

Considering the two optimised configurations with the two different aerofoils, Table 5 shows the respective data obtained with the optimisation performed. The $S{E^2}A$ optimised aerofoil permits to save more than 6% of the MTOW and a total drag reduction of at least 8%. This substantial reduction reflects the purpose of the whole project as stated in Section 1, complying with the Flightpath 2050 goals.

6.3 Power consumption and battery mass

The application of the Active Flow Control needs an extra amount of power than the functioning of the whole aircraft’s electric system without BLS. The integration of XFOILSUC and Q3D permits the power evaluation for each section in which the wing is divided to evaluate drag. The suction pump requires a power to restore the total head of the sucked air to that of the free stream, assuming an ideal scenario in which suction is continuous and the pump inlet pressure ( ${P_0}in$ ) as the boundary layer edge pressure [Reference Sudhi, Elham and Badrya24]. By applying the Bernoulli equation between freestream and edge of the boundary layer:

(8) \begin{align}C_{{DS}_{ideal}} = \int (1 - {C_P})\frac{{{v_o}}}{{{U_\infty }}}{\kern 1pt} d\left( {\frac{s}{c}} \right) \end{align}

Finally, the power for each aerofoil station is given by:

(9) \begin{align}Ps = C_{{DS}_{ideal}} \cdot 0.5 \cdot \rho \cdot V_\infty ^3 \end{align}

This required power, corrected for 80% efficiency, is shown in Fig. 17 for two different wings, one with NACA 65(2)415 and one with $S{E^2}A$ aerofoil.

The augmentation of the specific power per unit area at the tip ( $y = 1$ ) compared to the root ( $y = 0$ ), reflects the $C_{DS_{ideal}}$ increment along the stations (Fig. 18(a)). Wing suction involves about 30% of the local chord, Fig. 18(b) shows the actual power per unit length calculated per each aerofoil station, the area under the curve with respect to the span represents the whole wing power absorbed. Besides, the tip is a region with a high drag effect. Therefore, it requires more suction power, and profile drag presents an increment with respect to the root (for details see Section 6.5). The red curve in Fig. 17 represents the specific power absorbed for the optimised wing with $S{E^2}A$ aerofoil. For each station, the amount of power is lower than the optimised configuration with NACA 65(2)415 aerofoil. The $S{E^2}A$ aerofoil is obtained from a 2D optimisation for minimising drag and power consumption [Reference Sudhi, Elham and Badrya24], similar behaviour can be revealed for the wing application.

The power necessary for the BLS of the rest of the aircraft is obtained considering an average value of the specific power per area of the reference wing, and consequently, it is applied on the surface of the horizontal and vertical tail. The power absorbed for BLS of the fuselage is evaluated considering an analogous approach applied in Beck et al. [Reference Beck and Landa18] through XFOILSUC for laminar flow until wing junction (Table 6).

Table 6.

Total power for BLS

The battery mass obtained by the design range (see Section 5) and the modified Breguet Equation (7) can be appointed as system battery mass while the use of the BLS technology implies a power absorption and hence an extra mass that should be carried on board. Remembering the energy density ${E^*}$ = 464Wh/kg, the two contributes for both configurations are outlined in Table 7.

Figure 17.

Power evaluation for BLS of the two configuration: NACA 65(2)415 and $S{E^2}A$ .

Figure 18.

Power components investigation along the span.

Table 7 proves that the extra mass carried due to the BLS for almost 3 hours, seen as a payload mass represents only a small percentage ( $ \!\lt\!2\% $ ) of the battery mass necessary for the mission in a full-electric regional aircraft. In fact, the absorption of power for the active flow control, is an almost negligible fraction of the weight considering the strong drag reductions (see Section 6.5). In case the BLS system is not present, the aircraft will not have that weight contribute, but the limited percentage of weight does not compensate for the huge difference in the aerodynamics characteristics. In fact, only thanks to the BLS the aircraft can reach these high values of aerodynamic efficiency and hence satisfy the range top-level requirement keeping a limited maximum take-off weight (Table 5).

Table 7.

Battery mass contributes

6.4 Transition line

The activation of BLS moves the transition line back to approximately 80% of the local chord delaying the turbulence and hence gaining benefits from drag reduction. In particular, in Fig. 19 both wing configurations are displayed, clarifying the advantage of the Active Flow Control use. Figure 20 shows the variation of the transition line considering the BLS with respect to the reference wing and aerofoil (NACA 65(2)415 not optimised), relating the capability of the geometrical optimisation in delaying the transition. Hence, not only BLS may contribute to the shifting of the transition line, but also a different wing geometry can influence this position.

Figure 19.

Transition line variation for both wing configuration with and without BLS.

Figure 20.

Transition line variation for both wing configurations with BLS vs Reference.

Figure 21.

Transition line comparison for NACA 65(2)415 and $S{E^2}A$ , optimised vs reference with BLS.

The effect of the optimisation on the transition line is also proofed in Fig. 21, comparing all the configurations with the reference, with BLS working. The $S{E^2}A$ case has the transition line lying on the upper surface slightly forward than the NACA optimised case (Fig. 21(a)), however, it presents better performance. In fact, the SE²A aerofoil configuration reaches better performance with higher drag reduction thanks to a much higher portion of laminar flow on the bottom surface (Fig. 21(b)), hence the small difference of the transition position of the upper part makes not possible for the NACA configuration to compensate for the lower portion of laminar flow at the bottom surface. The optimiser, thanks to the lower profile drag for the SE²A aerofoil, tries to reach a configuration with a lower span (Fig. 15) to reduce wing weight and so higher reduction of the maximum take-off weight. The NACA optimised configuration presents higher laminar flow on the upper surface (Fig. 21(a)) but most of this advantage is affected by the lower portion on the bottom surface. Finally, the optimiser is looking for reducing drag incrementing the span and as consequence, the aspect ratio, acting on the induced drag. In this way, even if a bigger wing may lead to an increment of the weight, the effect is completely compensated by the better aerodynamics characteristics.

6.5 Boundary layer suction effect

The consequence of the BLS applied on the wing of the optimised aircraft with both wing configurations is outlined in terms of drag reduction in Table 8, proving the fundamental impact that active flow control technology plays. Optimised geometries are considered, and the application of BLS is observed compared to its non-functioning. The aircraft drag coefficient is evaluated taking into account $C_{{D}_{wing}}$ and the ${C_{D_{rest}}}$ obtained from the initial data and low fidelity analysis (see Sections 3 and 5), in particular for proper evaluation, initial data are used to obtain a new low fidelity aerodynamic efficiency, equal to $19.05$ , without BLS for the whole aircraft. Total drag is subjected to remarkable reduction with this technology because of the substantial role given by the $C_{{D}_{rest}}$ , which considers fuselage, horizontal and vertical tail. Activating BLS on the initial geometry (Table 1), the reduction of total drag is 43.55%, in line with preliminary low-fidelity results.

Table 8.

Boundary layer suction effect for optimised geometry

From an aerodynamic point of view, the distribution of the lift coefficient from root to tip (Fig. 22) of both aerofoils with BLS activated match perfectly the ${C_L}$ distribution in case of this technology turned off. In fact, the strategy is used only for the computation of drag, independently from the lift loads computation, as analysed in Fig. 10. The difference in the lift (Fig. 22) for the two configurations is caused by the different performance results of the optimised geometry, the $S{E^2}A$ configuration, reaching a higher MTOW reduction, exhibits a lower ${C_L}$ .

Figure 22.

Lift coefficient distribution for NACA 65(2)415 and $S{E^2}A$ , optimised, with/without BLS.

Hence, induced drag is overlapped according to the hypotheses formulated in the present work related to the aerodynamics analysis. The profile drag is sensitive to the activation of the BLS, and Fig. 23 shows clearly how the reduction of drag thanks to technology is relevant. Besides, NACA aerofoil is characterised by a higher total drag of the aircraft, in line with the previous statements. In case of failure of the BLS system at the beginning of the mission, considering the optimised configurations and applying Equation (7), the range is reduced similarly for both configurations of almost 46% with respect to the initial top-level requirement of 1,286km.

Figure 23.

Comparison of drag coefficients for the optimised wings with and without BLS.