Performance enhancement of a Box-Wing airliner with the application of riblets

The rapid growth of the commercial aviation sector in recent years, as well as the ambitious emission reduction targets, necessitate the investigation of novel methods to improve the aerodynamic efficiency of future airliners. With increasing passenger demand and evolving industry requirements, innovative designs, like the Box-Wing aircraft configuration, and flow control techniques, such as riblets, are essential to enhance efficiency, reduce fuel consumption and emissions, and meet future aviation needs. In this work, the performance enhancement of a novel Box-Wing airliner with the application of riblets is investigated through CFD modeling. The riblets are small, streamwise grooves aligned with the airflow, which when applied correctly, can reduce the turbulent skin friction drag. The riblets installed on the aircraft are modeled through a dedicated surrogate model, based on the cross-section area of their groove. In this study, both optimal size riblets, as well as constant size riblets, have been examined, assessing the performance degradation associated with the practical application limitations. The results show that the riblets can improve the aircraft’s aerodynamic characteristics, with a maximum drag reduction of 60 drag counts, as well as the overall flight performance, providing a maximum increase of 6.4% in payload and 13.3% in range.


Introduction
The current estimations about air traffic growth by IATA predict an average increase of about 4.4% per year [1], which makes evident the significant stress that the aeronautical sector will face, concerning its environmental impact.Globally, ambitious targets have been adopted by organizations and governments, concerning carbon dioxide (CO2) and nitrogen oxides (NOx) emissions, which in turn have resulted in the research and development of radical new technologies, related to topics such as aircraft engines, materials, and alternative fuels among others.However, a holistic approach is necessary if these targets are to be met since no single developed technology alone is sufficient [1].The main engineering goal of most of these new technologies is to reduce the fuel required, which from an aerodynamics point of view means that the drag force of the aircraft is reduced.This could be mainly achieved by adopting radical unconventional aircraft configurations that feature increased aerodynamic performance characteristics or by using flow control techniques that can improve the performance characteristics of a given aircraft.
The Box-Wing (BW) configuration is a concept first proposed by Prandtl in 1924, which features a close non-planar wing, and hence it offers reduced induced drag compared to conventional configurations with the same wingspan and same generated total lift.This reduction in induced drag is achieved by span efficiencies greater than unity, as shown by Kroo [2].Additionally, Demasi et al. [3] showed that the optimal lift distribution for a BW aircraft is not elliptical and varies with the distance between the fore (FW) and aft wing (AW).Also, the positioning of the FW and AW away from the aircraft's center of gravity provides additional benefits related to the pitch-damping moment, and thus trimming can be performed without any significant performance reduction.Regarding the main benefits of BW designs, they are mostly related to their superior performance compared to conventional aircraft, with similar span dimensions, and no dramatic deviation in design, by satisfying also current airport regulations and constraints.In terms of fuel-burn savings, those can be between 7% and 10%, for medium-range and long-range missions respectively, when considering maximum payload [1].Finally, the structural aspects of a BW design can result in a reduced overall wing weight [4].One of the challenges in BW designs is the distribution of fuel inside the wings, since the available space is lesser compared to conventional configurations, with an increased amount of fuel stored within the fuselage being a possible solution.Additionally, the aircraft's AF may suffer from different types of aeroelastic instabilities and fluttering, though dual fin configurations mitigate them to some extent [5].
Among the various flow control methods that have been investigated for aeronautical applications, the use of riblets has gained significant interest in the past few years [6], due to their ability to passively reduce the friction drag component of turbulent boundary layer flows.The riblets are small streamwisealigned micro-grooved geometries (in the order of 100-1,000μm) that affect the near wall region of the boundary layer with three distinct mechanisms: (a) by elevating upwards the cross-flow motion in their crests and displacing streamwise vortices and streaks away from the wall, (b) by weakening the nearwall turbulence regeneration cycle and (c) by dampening the spanwise flow fluctuations [7].However, they can also have a negative effect if they are inappropriately designed or placed, by amplifying the Tollmien-Schlichting waves and promoting premature boundary layer transition.The riblets have been investigated in the past both experimentally and numerically, though they require significant computational resources for LES or DNS simulations, with the main examined geometric parameters being the groove spacing  and the riblet height ℎ.A thorough review of earlier investigations concerning riblet application on aircraft can be found in the work of Viswanath [8].In 2022, riblet geometries were installed on the Boeing 777 fleet of Swiss airlines, marking their first large-scale application on a commercial aeronautical setting.To overcome the high computational cost associated with the simulation of riblets, various attempts have been made in recent years to incorporate the riblet effect in traditional RANS computations in the approach of surrogate modeling [9].
The present work focuses on two innovative concepts, the application of riblet geometries on a novel Box-Wing airliner, designed for medium-range missions.The effect of riblets is implemented numerically using a dedicated wall boundary condition for the specific turbulence dissipation rate .The drag reduction for the whole aircraft is evaluated in a range of angles of attack for cruise at Mach 0.78.The resultant performance gains for the aircraft are examined in two different scenarios, namely as an increase in payload and as an increase of the aircraft's operational range.This work aims to demonstrate the additional performance benefit that can be obtained by incorporating riblets on a novel aircraft concept, whose significant improvements compared to conventional airliners have been previously presented [10].

Box-wing reference aircraft
The aircraft, that serves as the reference platform on which riblets are applied, is a novel Box-Wing airliner, designed by the Aristotle University of Thessaloniki and is described in detail in the work of Kaparos et al. [10].The BW reference aircraft is a medium-range airliner, whose design was based on the Airbus A320-200 mission characteristics, which is its main competitor.The BW aircraft features a continuous-surface non-planar wing formation without wingtips, which can be subdivided into a fore (FW) and an aft wing (AW), connected with an almost vertical fin.The lift is produced equally by the FW and AW, and their corresponding sweep and incidence angles are defined by both structural and stability considerations.The resulting dimensions of the BW aircraft are very close to those of the A320-200, to comply with airport regulations and constraints, and a comparison of the two aircraft is presented in Figure 1.The aircraft is designed to operate at Mach 0.78, cruise altitude between 35,000-40,000ft and with a capacity of 180 PAX.In terms of performance, the BW aircraft features an increased Oswald factor, a reduced gross take-off weight (GTOW), as well as a reduced induced drag component (-12.5%),compared to the Airbus A320-200.

CFD methodology
All analyses on the BW aircraft are performed numerically, by solving the steady Reynolds-averaged Navier-Stokes (RANS) equations, since the aircraft's operational angles of attack were relatively small, and no stalling or other unsteady phenomena are present.For the turbulence modeling, the two-equation shear stress transport (SST) k-ω turbulence model is employed.The turbulence model is selected based on its robustness and ability to accurately capture the turbulence effects in flows with adverse pressure gradients, as well as due to the requirement for an adoption of a riblet surrogate model for a k-ω family model.
The computational meshes are produced using the BETA ANSA pre-processing software (v23.1.0,Root, Switzerland).Each unstructured computational mesh has a structured layout region near the solid surfaces of the aircraft, where the boundary layer develops, with 25 cells in the normal to the wall direction.To ensure that the  + is maintained everywhere below unity and that at least 5 computational cells lay within the viscous sublayer, an appropriate first cell height and a growth ratio of 1.1 are selected.The computational mesh used for the CFD analyses is the result of a thorough grid independency study, performed for the mid-cruise flight conditions and by using the drag coefficient as the primary monitor variable.To quantify the result changes from the different mesh refinements, the Grid Convergence Index (GCI) is used [11], with the resulting values presented in Table 1.The G3 mesh (Table 1) is selected for all analyses since further grid refinement does not result in any significant change in the aircraft's drag, and also to reduce the computational cost.
The solution is performed with the ANSYS Fluent 2020R2 (Academic Multiphysics Campus Solution, Canonsburg, PA, USA) software, using a density-based implicit solver along with the improved advection upstream splitting method (AUSM+) and the Green-Gauss cell-based gradient method, for the flux vector and gradients calculation respectively.The third-order MUSCL scheme is employed for the discretization of all the partial differential equations.This numerical setup has been previously successfully employed in the modeling of aircraft operating in the transonic and supersonic flight regimes [12].

Modelling of riblets
The effect of riblets is incorporated in the numerical computations, through surrogate modeling.More specifically, the method proposed by Mele and Tognaccini [13] is used, where the original boundary condition of the turbulence dissipation rate  (Equation 1), for the k-ω family of turbulence models, is altered.
The parameter   in the original boundary condition proposed by Saffman [14] depends on the nature of the wall and can be used to model the roughness of different wall types (as a function of the roughness Reynolds number   + ) or riblets.To model the effect of riblets, Catalano et al. [15] proposed an algebraic relationship for   (Equation 2) which is based on the non-dimensional root of the riblet groove crosssection   + .This relationship is the result of a bell-type curve fitting on the experimental data presented by Garcia-Mayoral and Jimenez [16] and has been successfully implemented in cases related to airfoils, conventional regional airliners, and UAVs [15,17,18].The curve fitting parameters  1 ,  2 ,  3 , and  are equal to 2.5×10 8 , 10.5, 10 -3 , and 3, respectively.
To apply the effect of riblets on the BW aircraft correctly, the areas where the boundary layer has transitioned to fully turbulent are first identified.Towards that, dedicated CFD computations are performed, as described in section 2.2, but the three-equation    turbulence model is employed instead.This turbulence model along with the transport equations for the turbulent kinetic energy  and the specific turbulence dissipation rate , includes also the transport equation for the energy of nonturbulent fluctuations   (laminar kinetic energy).The model utilizes local flow variables and can be employed for the prediction of both natural and by-pass transition.Its capability to accurately predict the transition of the boundary layer has been previously validated with experimental results for flows over flat plates under adverse, zero and favorable pressure gradients, around typical airfoils and turbine blade cascades [19].In order to identify the transition point, the distribution of the skin friction coefficient is examined on the planes presented in Figure 2a.Additionally, the shape factor  12 is also computed in these points to validate the planes' selection.Based on these findings, the areas where riblets will be applied are identified (Figure 2b), ensuring that the flow in these locations is fully turbulent and that no negative effects (e.g., premature boundary layer transition) from the use of riblets will arise.
In these areas, two different approaches for riblets are examined.Firstly, optimal riblet sizing is examined, where the value of   + is kept everywhere equal to 10.5.In this approach, the maximum possible performance gain from riblets is calculated, with the actual riblet size   (Figure 3) varying with the local flow conditions (i.e.cell local   ).This approach results in different riblet dimensions (  ) on each computational cell of the aircraft's surfaces.The second approach of discrete riblet sizing is also examined, because, in certain cases, the optimal riblet sizing can produce unrealistic riblet distributions on the surfaces of an aircraft.In this approach the areas of the BW aircraft are divided into smaller ones, on each of which the wall shear stress is relatively constant.On each examined surface area, a constant riblet dimension (  ) is applied, corresponding to the optimal value based on the area's mean wall shear stress.In Figures 4a and 4b, the implementation of the surrogate model is presented for optimal and discrete riblet sizing, respectively.

Results
To evaluate the potential of riblets, it is worthwhile to compute and present the contribution of the viscous phenomena to the total drag of the aircraft (Figure 5).It is observed that for angles of attack (AoA) close to zero, the viscous drag component accounts for 20%-30% of the total aircraft drag, and hence, in these conditions the riblets are expected to have the most significant effect.This is also evident from the results of Table 2, for both the optimal and discrete size riblets, where the drag reduction in total drag counts is larger in small AoA and also far more significant in percentage terms.As an example, we observe that for optimal riblets application, the drag reduction is more than doubled in absolute values between 6° and 10°, while the percentage remains almost constant, as the pressure drag component contribution becomes more prominent in higher AoA.Moreover, the discrete size riblets produce a significantly smaller drag reduction, compared to the optimal sized ones, since the constant size of riblets over a specific surface, can result also in a drag increase on certain areas where the flow conditions deviate significantly from the surface's average values.In Figures 6 and 7, the skin friction coefficient distribution on the fore and aft wings is presented for the case without riblets, with discrete size riblets, and with optimal size riblets, at 0° (a) and 8° AoA (b), for flight conditions corresponding to the cruise Mach number of 0.78.The differences in skin friction values are relatively small between the case without riblets and that with discrete size ones, in agreement with the results of drag count reduction in Table 2.However, the optimal size riblet case features significantly smaller skin friction coefficients, which can most notably be observed at the 0° AoA (Figure 6a and Figure 7a).Additionally, the results of the 8° AoA cases showcase the notable deterioration of riblet performance at higher AoA, hence highlighting the importance of riblet sizing at the appropriate flight conditions.The drag reduction due to riblet application can be expressed in terms of performance gains for the actual aircraft.Two different scenarios are examined, in both of which the GTOW of the aircraft is maintained constant.In the first scenario, the fuel weight value is considered fixed, and the resultant drag reduction is translated into an increased range as computed by the Breguet equation (Equation 3).The use of discrete size riblets can improve the aircraft's range by 3.8%, while the optimal size riblets can offer a 13.3% increase (Table 3).In the second scenario, the range is kept constant, and the excess fuel weight is replaced by additional payload.The discrete riblets allow the payload to be increased by 1.8% (310 kg), and the optimal riblets by 6.4% (1070 kg).

Conclusions
In this work, the numerical investigation of riblets on a novel Box-Wing airliner was examined.The riblets installation on the aircraft are modeled with CFD analyses, by adopting a dedicated surrogate model, that alters the  boundary condition.Two types of riblet cases were applied on the aircraft, discrete sized and optimal sized ones.The use of riblets showed a noticeable effect on AoA close to 0°, which diminishes as the AoA is increased, due to the decrease of the viscous drag component contribution to the aircraft's total drag.The optimal size riblets provided a maximum drag reduction of 60 drag counts, while the discrete ones of 18 drag counts.The effect of riblets on the performance of the aircraft was also assessed, where an increase in the aircraft's range of 3.8% and 13.3% for the discrete and optimal size riblets was shown.Additionally, if the aircraft's range is kept constant, a payload increase of 1.8% and 6.4% can be achieved, for the two riblet cases, respectively.As a final comment, it has been demonstrated that riblets can be an effective flow control method, with a great potential to significant fuel savings and performance increase for a Box-Wing airliner.

Figure 1 .
Figure 1.Geometrical characteristics of the BW aircraft, compared to the Airbus A320-200.2.2.CFD methodologyAll analyses on the BW aircraft are performed numerically, by solving the steady Reynolds-averaged Navier-Stokes (RANS) equations, since the aircraft's operational angles of attack were relatively small, and no stalling or other unsteady phenomena are present.For the turbulence modeling, the two-equation shear stress transport (SST) k-ω turbulence model is employed.The turbulence model is selected based on its robustness and ability to accurately capture the turbulence effects in flows with adverse pressure gradients, as well as due to the requirement for an adoption of a riblet surrogate model for a k-ω family model.The computational meshes are produced using the BETA ANSA pre-processing software (v23.1.0,Root, Switzerland).Each unstructured computational mesh has a structured layout region near the solid surfaces of the aircraft, where the boundary layer develops, with 25 cells in the normal to the wall direction.To ensure that the  + is maintained everywhere below unity and that at least 5 computational cells lay within the viscous sublayer, an appropriate first cell height and a growth ratio of 1.1 are selected.The computational mesh used for the CFD analyses is the result of a thorough grid independency study, performed for the mid-cruise flight conditions and by using the drag coefficient as the primary monitor variable.To quantify the result changes from the different mesh refinements, the Grid Convergence Index (GCI) is used[11], with the resulting values presented in Table1.The G3 mesh (Table1) is selected for all analyses since further grid refinement does not result in any significant change in the aircraft's drag, and also to reduce the computational cost.The solution is performed with the ANSYS Fluent 2020R2 (Academic Multiphysics Campus Solution, Canonsburg, PA, USA) software, using a density-based implicit solver along with the improved advection upstream splitting method (AUSM+) and the Green-Gauss cell-based gradient method, for the flux vector and gradients calculation respectively.The third-order MUSCL scheme is employed for the discretization of all the partial differential equations.This numerical setup has been

Figure 2 .
Figure 2. (a) The planes on which boundary layer transition is examined and (b) the resulting areas on which riblets are applied.

Figure 3 .
Figure 3.Typical riblet geometries and their basic geometric parameters.

Figure 4 .
Figure 4. Flow chart of the surrogate model for (a) optimal and (b) discrete riblet size.

Table 1 .
Grid Convergence Index of the grid independency study.

Table 2 .
Contribution of viscous drag component to the aircraft's total drag for a range of AoA.Drag reduction on the aircraft from the application of riblets.

Table 3 .
Aircraft performance increase from the riblet application.