Drag bookkeeping on an aircraft with riblets and NLF control

Aerospace Science and Technology 98 (2020) 105714

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Drag bookkeeping on an aircraft with riblets and NLF control Benedetto Mele ∗ , Lorenzo Russo, Renato Tognaccini Department of Industrial Engineering, University of Naples Federico II, P.zzle Tecchio 80, Naples, Italy

a r t i c l e

i n f o

Article history: Received 27 July 2019 Received in revised form 3 December 2019 Accepted 15 January 2020 Available online 22 January 2020 Communicated by Damiano Casalino Keywords: Aerodynamic force breakdown Riblets NLF

a b s t r a c t In the frame of aerodynamic drag reduction for low-emission target, Natural Laminar Flow (NLF) control and riblets are the most interesting passive techniques. The drag breakdown in the case of riblets installed is a topical matter for understanding on which form of drag riblets act. Indeed, linear theories and flatplate experiments show that riblets act on friction drag whereas other experiments in pressure-gradient flow revealed an increased performance of riblets that was not interpreted. A contribution to clarify this effect has been recently provided analyzing the effect of riblets on form drag in two-dimensional pressure-gradient flows. In the present paper the effect of riblets on pressure drag is discussed also in three-dimensional flows analyzing CFD solutions of the flow around an innovative regional turbo-prop aircraft (wing-body configuration) with NLF and riblets installed. For the first time, the contribution of each of two drag reduction systems is identified and a deep analysis on which form of drag riblets act in three-dimensional flow is proposed thanks to a far-field aerodynamic drag breakdown. © 2020 Elsevier Masson SAS. All rights reserved.

1. Introduction In the recent years, the requirement of reduction of pollutant emission led to an increasing interest in drag reduction that has become a keyword for the next generation aircraft and in general for lifting bodies [1–5]. Natural Laminar Flow (NLF) control and riblets are probably the most interesting passive drag reduction techniques. NLF is based on the particular design of wing sections. Although NLF airfoils were widely studied since the forties, when NACA developed the well known 6-series airfoil family, characterized by high performance in controlled wind tunnel experiments; laminar flow was hard to be maintained in operative conditions due to the contamination in the leading edge region. The success of the NACA 6-series family was more related to the good highspeed performance rather than to the laminar capabilities. More advanced NLF airfoils have been designed in the last years [6,7] with improved performance and less side effects, providing the opportunity to adopt this technology in general aviation and, in particular, for business jet application. Nonetheless, the successful cases have been limited to the case of unswept wing, because of the well known cross-flow instability. Riblets consist of streamwise grooved surfaces able to reduce friction drag in turbulent flow. Due to riblets dimensions (micron in aeronautical applications) only DNS or LES should be adopted for explicitly capturing drag reduction mechanism due to riblets

*

Corresponding author. E-mail address: [email protected] (B. Mele).

https://doi.org/10.1016/j.ast.2020.105714 1270-9638/© 2020 Elsevier Masson SAS. All rights reserved.

but, these types of computations are still unfeasible for complex aeronautical configurations. In order to overcome this problem, some models for riblets effect simulations at high Reynolds numbers flows have been recently developed. Aupoix et al. [8] modified the equation of the Spalart-Allmaras turbulence model to take into account the effect of riblets. Following a different approach, Mele & Tognaccini [9] proposed a boundary condition for the k − ω turbulence models that turned out to be an efficient method for the numerical simulation of riblets able to calculate riblet performance in complex aeronautical configurations [10]. Koepplin et al. [11] proposed a modification of the model of Aupoix et al. to analyze the effect of misalignment of riblets in pressure gradient flows. Each cited model has been developed to mimic the effect of riblets in the flow field without inserting riblets geometry in the computational domain (i.e. the walls where riblets are adopted are smooth). The effect of riblets in pressure gradient flow is still a debated subject; indeed, even if the analyses based on linear theories [12] and the experiments conducted for flat plate flow [13] showed that riblets effect is essentially local (i.e. it depends on the local Reynolds number), experiments and computations [14–17] in adverse pressure-gradient flows showed an increased effectiveness of riblets, an effect not explained so far. Very recently, Mele & Tognaccini [18] contributed to clarify this result developing a new model based on the slip-length concept. They found that riblets have a secondary but significant effect on form drag and provided also a quantitative analyses by the classical matched asymptotic expansion theory that showed that riblets reduce the displacement

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thickness leading to a reduction of the form drag. This mechanism was also measured in an experiment of flat plate in adverse pressure-gradient flow [16]. In Clean Sky 2 IRON EU funded research project, the design of an innovative turbo-prop aircraft is being studied. NLF control is proposed on the innovative configuration and also the assessment of the effect of riblets installation over the turbulent part of wings and fuselage has been planned. In this frame the bookkeeping of drag reduction due to the combined effect of NLF control and riblets is a relevant topic. In particular, the effect of riblets on the different drag components (friction, form and lift induced drag) is worth of investigation. For this purpose, a drag breakdown, available only by far-field methods in three-dimensional flows, is required. The analysis and breakdown of the aerodynamic force in its physical contributions is an important subject for both theoretical knowledge and industrial applications. A detailed characterization of the aerodynamic force sources and variation, particularly in high-transonic and supersonic flows, is a valid means for aerodynamic optimization and drag reduction, which is today a critical issue for low-emission target of the next-generation aircraft. The classical definition of the aerodynamic force as the integral of fluid stresses acting on a moving body immersed in a fluid (near field method) allows only for a distinction between friction and pressure drag. The problem is further complicated when compressible effects, such as shock waves, are present in the flow. The integral momentum equation allows for a definition of the aerodynamic force integrating momentum flux on a surface enclosing the body and far from the configuration (far-field methods). A further possibility is to reduce the force computation to volume integrals of the flow properties non negligible only in limited parts of the domain (such as entropy variation). These techniques are better referenced as mid-field methods and give the chance to decompose the aerodynamic drag in viscous and wave components. The interest in these methods is also given by the possibility to relate the source of the aerodynamic force to local flow properties in view of a possible aerodynamic optimization or flow control. Techniques based on the entropy drag concept are now widely adopted [19–27]. These are mid-field methods since rely on the entropy production associated with the dissipative phenomena in the body boundary layer and shock waves. Vorticity is another flow property non negligible in a limited part of the flow domain. Many methods have been derived to compute the aerodynamic force in terms of vorticity integrals. Probably the most known is Maskell’s formula [28] for the computation of lift-induced drag by wake survey of vorticity field behind a wing. The so-called Lamb vector field is related to vorticity and defined as the cross product of vorticity times velocity:  = ω × V . The idea of its link with the aerodynamic force dates back to Prandtl. Von Karman and Burgers, introduced the concept of vortex force defined as the volume integral of the Lamb vector distribution. The vortex force and its relation with aerodynamic force has been successively discussed by Saffman [29] in incompressible flow with bounded vorticity and by Wu et al. [30] who overcame the mathematical difficulties in the application of the vortex force concept to flows with unbounded vorticity fields. In [31,32] and [33,34], the method has been extended to high Reynolds number, turbulent and compressible flows also providing a decomposition for liftinduced drag. In [35,36] and [37] the Lamb-vector based method has been extended to unsteady flows and applied to oscillating body. In the present paper the aerodynamic analysis of the flow around an advanced regional turbo-prop aircraft (wing-body configuration) with NLF and riblets installed is performed by CFD simulations. The drag reduction achievable by riblets installation is computed using the method described by Mele et al. in [10]. A

comparison between the two drag reduction techniques (NFL and riblets) is provided together with the effect in terms of drag reduction of their combined application. The decomposition of the drag reduction obtained by riblets in its physical contributions is finally performed adopting a far-field method that is the only way to obtain a breakdown of drag in viscous (friction and form), wave and lift-induced drag in three-dimensional flows. The analysis provides, for the first time, an insight into the effect of riblets in 3D pressure gradient flows. 2. Modelling riblets performance at high Reynolds numbers The models which will be here adopted for riblets performance computations are described in details in [10] and [18]; in this section the models’ main formulae are briefly recalled. Both models replicate the effect of riblets on logarithmic law of wall. It has been shown [13,12] that riblets induce a shift in the origin of the velocity profile (i.e. a shift of the constant of the log law). The two models for riblets simulations reproduce this effect by boundary conditions applied at the wall. The first model proposes a boundary condition for the k − ω turbulence models family [9,10]. It is based on the boundary condition introduced by Saffman [38]:

ω=

ρ u 2τ μ

SR =

τw S R (k+ s ), μ

(1)

√

where ρ is the density, u τ = τ w /ρ is the friction velocity (τ w is the wall shear stress) and μ is the dynamic viscosity. S R is an unknown function that depends on the nature of the wall and, as shown in [39], its value (and thus the value of ω at the wall) determines the value of the constant in the log law. We derived and ad-hoc expression for S R in case of riblets:

SR =

C1 2n + C (l+ 3 g − C2)

(2)

.

Equation (2) is written as a function of l+ g =



+ A+ g , where A g is

the riblet non dimensional cross section area that can be used to simulate the effects of an arbitrary riblet family. The coefficients have been obtained by numerical experiments matching the experimental data reported in [40]: C 1 = 2.5 · 108 ; C 2 = 10.5; C 3 = 1. The boundary condition has been widely validated in flat plate and airfoil flows comparing numerical computation with available experiments as shown in [9,10]. Very recently a new model based on slip length concept has been developed. The model, described in [18], proposes the adoption of a slip boundary condition that can be substantially applied to all flow types that can be modelled by a shift (U + ) of the reference surface (i.e. shift of the constant of log law). The slip boundary condition relates the components of the velocity tangent to the surface u w to the shear rate at the surface (∂ u /∂ y ) w by means the so-called slip length λ. In the case of a two-dimensional flat plate:

 uw = λ

∂u ∂y

 (3) w

In case of riblets λ = h, the difference between longitudinal and transverse protrusion height [12]. Thus, the following relation between riblets dimensions (l+ g ) and λ, here expressed in terms of Re λ (l+ ) , has been derived. g

C1  − λ0 , Re λ =  2 + l g − 10.5 + C 2

(4)

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where C 1 = 170, C 2 = 10.0 and λ0 = C 1 /(10.52 + C 2 ) whereas Re λ is the Reynolds number based on λ. Being not linked to a turbulence model, this boundary condition overcomes some limitations of (2) and allows for an explanation of the effect of riblets in pressure gradient flow which is discussed in the next section. 3. Riblets in pressure gradient flows During the 90’s, some experimental campaigns [17] showed that drag reduction due to riblets increased with the angle of attack in subsonic conditions. Debisschop & Nieuwstadt [16] verified the improved efficiency of riblets in a flat plate flow in adverse pressure gradient measuring also a decrease of displacement thickness. More recently, Boomsma and Sotiropoulos [14] performed LES simulations of flat plate flow with zero and mild adverse pressure gradient. They found an increased drag reduction of 1 − 1.5% at a Clauser’s parameter equal to 0.5 than in the case of zero pressure-gradient flow. Zhang et al. [41] performed an Implicit LES simulation on an airfoil and found an increased lift and a decreased friction drag with riblets installed. Very recently Mele and Tognaccini [18] proposed an explanation for the increase of riblets performance in pressure-gradient flows; the essential results are here reported. Even if the pressure gradient doesn’t affect the log law, the boundary layer developing with the modified U + has a secondary influence on the outer inviscid flow and pressure distribution, as well known by Prandtl’s boundary layer theory. In Fig. 1 a comparison between the numerical and experimental results obtained for a NACA 0012 and a GAW(2) airfoil covered by riblets are shown. The experiments reported an increasing efficiency of riblets with the angle of attack and suggested that the pressure distribution affects riblets performance. CFD simulations, performed adopting the same riblet height (0.152mm) and span as in the experiments, confirmed the experimental results. Decomposing the drag in friction and pressure contributions it was noted an unexpected reduction of the pressure drag which implies a reduction of the form drag due to riblets. This phenomenon is due to riblets effect on both the pressure recovery at the trailing edge and the expansion peak. A quantitative analysis of this effect can be performed with the help of the classical matched asymptotic expansion technique. The boundary layer influence on the second order outer expansion is given by the boundary condition on the normal velocity at the wall, producing the blowing of the boundary layer in the outer flow [42] p. 381:

V 2 (x, 0) =

d dx

[U e (x)δ ∗ (x)] .

(5)

In this equation x is the coordinate tangential to the wall, U e (x) is the tangential velocity on the wall obtained by the first order outer expansion (inviscid solution) and δ ∗ (x) is the boundary layer displacement thickness given by the first order inner expansion. U e (x) and δ ∗ (x) can also be computed by post-processing CFD solutions. Indeed, known the pressure field p (x, y ), the first order outer expansion of pressure at the wall is p e (x) ≈ p (x, 0) and, since the subsonic outer flow is isoentropic and isoenthalpic (γ is the ratio of specific heats):



ρe (x) ≈

p e (x) p∞



(1/γ ) ,

U e (x) ≈ ∗

2 + V∞

∞

δ (x) = 0

2γ

γ −1

1−

p e (x)

ρe (x)

,



ρ (x, y )u (x, y ) 1− dy . ρe (x)U e (x, y ) (6)

Fig. 1. Drag reduction vs. angle of attack, Re ∞ = 106 , M ∞ = 0.1. NACA 0012 airfoil (a) and GAW(2) airfoil (b).

Fig. 2 reports the computed δ ∗ (x) at α = 0 and α = 6deg. Both displacement thickness and boundary layer blowing (here not displayed) are lower when riblets are installed. The reduced thickness of the equivalent body due to the boundary layer is the reason why the form drag decreases. The reduction of the boundary layer blowing is much more marked at α = 6deg and this is very likely the reason why the riblets performance increases, as evidenced also by the experiments. In practice, the form drag decreases when riblets are installed because the pressure distribution moves towards the inviscid one, characterized by zero form drag. In the next sections the effect of riblets on form drag will be analyzed in 3D flows with the help of drag breakdown performed by a far-field method. 4. Aerodynamic performance of NLF wing body configuration with riblets RANS CFD simulations on an advanced turbo-prop (wing-body configuration) have been carried out adopting the flow solver FLOWer developed at DLR (the German Aerospace Center) and modified for riblets simulations. The code solves the compressible three-dimensional steady and unsteady RANS equations on block-structured meshes around complex aerodynamic configurations. The spatial discretization adopted was a central finite volume formulation with explicit blended 2nd and 4th order artificial dissipation. Time integration is carried out by an explicit hybrid multistage Runge-Kutta scheme. The k − ω SST LR turbulence

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Fig. 3. Wing-body geometry.

Fig. 2. NACA 0012 Airfoil, Re ∞ = 106 , M ∞ = 0.1. Computed distribution of displacement thickness along the suction side of the airfoil with and without riblets at α = 0◦ (a) and α = 6◦ (b).

model [43,44], modified for considering riblets [9,10], was adopted. The same numerical scheme and settings have been adopted with and without riblets installed and also in the case of NLF control. A structured mesh with 147 block and 40 millions cells in the finest grid level has been used. The design of the NLF wing has been performed at CIRA (the Italian Aerospace Center) adopting methods similar to that described in [7]. The aircraft is designed to have natural laminar flow for a large extent of the wing in cruise condition. In Fig. 3 the analysed wing-body geometry is shown. Numerical simulations have been performed at Reynolds number Re ∞ = 18.2e + 6, M ∞ = 0.64, α = −2, 0, 2, 4deg. The laminarturbulent transition point has not been explicitly computed but it has been imposed using data provided by the designers of the wing. Riblets were then installed only in the turbulent part of the wing and on whole fuselage. Numerical simulations with riblets have been performed at l+ g = 10.5, this means that an optimal riblet height distribution is adopted over wing-body surface. In the case of standard riblet family with a symmetric V-grooved section, √ + and h + is s+ = h + = 2l+ . Indeed, the relation between l+ g, s g one of the advantages of the present model is that the optimal riblet height distribution can be retrieved as a result of the numerical simulations. However, it must be remarked that, as shown in a previous work [10], the drag reduction obtained adopting riblets with constant height and with optimal height distribution, is almost the same.

Fig. 4. Wing body Re ∞ = 18.2 × 106 , M ∞ = 0.64, coefficients.

α = 0◦ . Wing section pressure

The turbulence model is adopted in the whole flow field; the laminar condition is obtained by switching off the turbulence production [45]. Since the wing sweep angle is small, the laminar zone on the wing has been estimated performing a two-dimensional stability analysis by an en method on six wing sections, then a linear interpolation has been adopted. In Fig. 4 the computed pressure coefficients in fully turbulent flow at α = 0deg on the six wing sections considered for stability analysis are shown. It is worth noting that the transition points are correctly estimated in the adverse pressure gradient zone. In Fig. 5 the wing body configuration is shown with pressure coefficient distribution on the body and the module of x-vorticity in the wake whereas in Fig. 6 the adopted laminar and turbulent zones are displayed on upper and lower body surfaces. A convergence analysis while reducing the mesh size has been firstly performed. In Figs. 7 and 8 the polar curves without and with riblets are reported for three grid levels, h = 1 is the finest grid level; it can be noted that the results of the grid conver-

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Fig. 5. Wing body: M ∞ = 0.64, Re ∞ = 18.2 × 106 , α = 0◦ , fully turbulent, riblets off. Pressure coefficient distribution and x-vorticity module in the wake.

gence analyses are substantially the same with and without riblets. The convergence analysis while reducing mesh size shows that the medium grid returns a good accuracy and will be used in the next analyses. In Fig. 9 the y + distribution for h = 2 grid is reported showing that y + is well below the unity almost everywhere on wing body surface. Fig. 10 shows the computed drag reduction in counts (C D × 104 ) obtained thanks to riblets installation at three different mesh size together with a zero mesh size extrapolation. It can be seen that also in the case of riblets installed the calculations are converging while reducing the mesh size and that the difference between h = 2 mesh and h = 1 mesh in terms of drag reduction is less than 2 drag counts. Riblet effect can be appreciated in Fig. 11 where the polar curves with and without flow control are shown. The effect of riblets is evident also in case of NLF control. The variation of drag reduction with the angle of attack is shown in Figs. 12 and 13. It is worth noting that, while the friction drag reduction is substantially constant while varying the angle of attack, the total drag reduction decreases. This effect is linked to the increase of lift-induced drag while increasing the angle of attack. The net effect of riblets should be appreciated just by the friction drag reduction. Fig. 14 shows the skin friction distribution over the body with and without riblets and highlights their effect. In Fig. 15 the computed optimum riblet height distribution is shown, considering symmetric sawtooth riblets. It can be seen that optimum riblet height is about 70 microns on the wing and 80-90 microns on the fuselage. Finally in Fig. 16 the bookkeeping of drag reduction is reported showing that the drag coefficient can be reduced by almost 40 counts adopting riblets together with NLF technology. 5. Analysis of drag reduction components In this section the drag breakdown by an entropy-based method is proposed for the wing-body configuration with and without riblets and NLF technologies installed. 5.1. Entropy-based drag breakdown method For the drag breakdown of the wing-body configuration the far field method proposed by Paparone and Tognaccini, described in [19], will be adopted; its fundamental formulae are here briefly recalled.

Fig. 6. Wing body: M ∞ = 0.64, Re ∞ = 18.2 × 106 , α = 0◦ . Laminar-turbulent zones. Blue: laminar, red: turbulent. (a) Upper skin, (b) lower skin. (For interpretation of the colours in the figure(s), the reader is referred to the web version of this article.)

A turbulent, steady high-Reynolds number compressible flow around an aircraft configuration is considered. Assuming a cartesian reference system with the x axis aligned with the asymptotic velocity, a straightforward application of the momentum balance equation provides the far field drag expression:



D f ar = −

[ρ u (V · n) + ( p − p ∞ )nx ] dS ,

(7)

S f ar

where ρ is the fluid density, V = [u , v , w ] T is the local velocity, p is the pressure and subscript ∞ specifies free-stream conditions. S f ar is the outer boundary of the computational domain, n = [nx , n y , n z ] T is the unit normal vector pointing outside the computational domain. Expanding in Taylor’s series the axial velocity defect expression with respect to the entropy variation s =

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Fig. 7. Wing body: M ∞ = 0.64, Re ∞ = 18.2 × 106 , fully turbulent, riblets off. Liftdrag polar curves obtained on three grid levels.

Fig. 8. Wing body: M ∞ = 0.64, Re ∞ = 18.2 × 106 , fully turbulent, riblets on. Liftdrag polar curves obtained on three grid levels.

s − s∞ and taking into account for second order terms at most, the entropy drag expression is obtained:



D s = − V ∞

∇ · [ρ g (s)V] d ,

(8)



where  is the flow domain and

 g (s) = f s1

s R



 + f s2

s R

2 (9)

,

with R that is the gas constant and the coefficients f s1 and f s2 given by

f s1 = −

1 2 γ M∞

,

f s2 = −

2 1 + (γ − 1) M ∞ 4 2γ 2 M ∞

(M ∞ is the free-stream Mach number and heats).

Fig. 9. Wing body: M ∞ = 0.64, Re ∞ = 18.2 × 106 , α = 0◦ , fully turbulent. y + distribution on the body, medium grid: h = 2. (a) Upper skin, (b) lower skin.

The entropy drag takes into account for the contributions associated with irreversible processes: viscous and wave drag. The

domain  can be decomposed as  =  visc sw sp , where  visc is the boundary layer and the wake regions, sw is the shock wave region, and sp is the remaining part of the flow field. Therefore, the entropy drag can be decomposed in three components:

D visc = V ∞

,

(10)

γ is the ratio of specific

  ∇ · ρ gV d ,

 visc



Dw = V∞ sw

  ∇ · ρ gV d ,

(11)

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Fig. 10. Wing body: M ∞ = 0.64, Re ∞ = 18.2 × 106 , α = 0◦ , fully turbulent. Computed Drag reduction due to riblets against mesh size of the adopted grid (optimum height distribution on wing and fuselage). h = 1: fine grid.

Fig. 12. Wing body: M ∞ = 0.64, Re ∞ = 18.2 × 106 , fully turbulent, h = 2 grid. Drag reduction due to riblets vs angle of attack (optimum height distribution on wing and fuselage). Reference value in percentages is smooth condition.

Fig. 11. Wing body: M ∞ = 0.64, Re ∞ = 18.2 × 106 , h = 2 grid. Lift drag polar curves with and without riblets (optimum height distribution on wing and fuselage).

Fig. 13. Wing body: M ∞ = 0.64, Re ∞ = 18.2 × 106 , NLF h = 2 grid. Drag reduction due to riblets vs angle of attack (optimum height distribution on wing and fuselage). Reference value in percentages is smooth condition.

D sp = V ∞

  ∇ · ρ gV d .

sp

D visc is the viscous drag, D w is the wave drag and D sp is the spurious drag component, linked to the numerical dissipation introduced by the numerical schemes that lead to an nonphysical drag contribution. It is clear that the breakdown method relies on a proper selection of the three domains  visc , sw and sp . This is performed by the definition of boundary layer and shock wave sensors discussed in [19] and [23]. Finally the lift induced drag is computed by the classical Maskell formula [28] 5.2. Drag decomposition In Fig. 17 the grid convergence analysis in terms of near field and far-field drag (entropy drag without spurious drag) is shown in case of cruise condition with riblets installed. The results show

that the far field method provides already converged results with the h = 2 grid. The removal of the spurious contribution permits to obtain satisfactory results even with h = 4 grid. Therefore, further applications of the drag decomposition method will be proposed for the h = 2 grid. The drag decomposition is reported in the present section starting from the analysis of fully turbulent flow (no NLF control) with and without riblets, as shown in Figs. 18 and 19 for the h = 2 grid. The near field drag is also reported, 8 drag counts of spurious drag have been detected in both the cases showing that the model for riblets simulation does not introduce further artificial dissipation. It can be seen that the riblets substantially act only on the viscous drag, indeed the lift induced drag is the same with and without riblets, as expected (except for a slight increase due to the lightly augmented lift coefficient at the same incidences). The analysis of the wave drag component computed at α = 4deg, where transonic flow occurs, shows another interesting riblets effect: a comparison between the detected wave drag with

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Fig. 15. Wing body: Re ∞ = 18.2 × 106 , M ∞ = 0.64, α = 0◦ . Computed optimal riblet height distribution (symmetric sawtooth riblets). (a) Upper skin, (b) lower skin. Fig. 14. Wing body: Re ∞ = 18.2 × 106 , M ∞ = 0.64, α = 0◦ . Skin friction coefficient with and without riblets. (a) Upper skin, (b) lower skin.

and without riblets reveals that (even if small), the wave drag increases of almost 30% in case of riblets installed. This effect was already discussed analyzing a flow around the RAE 2822 airfoil [10]. In the proposed solutions, a shock induced separation was obtained in presence of riblets. Unfortunately there are not experimental data to compare this effect but it is reasonable that the lower turbulence levels induced by riblets increases the intensity of the shock wave. Indeed, the lift coefficient was also slightly increased by riblets. In Figs. 20 and 21, where the viscous drag decomposition is reported, the effect of riblets on form drag can be appreciated. There is an evident reduction of form drag due to riblets except at

C L = 1.08 where form drag slightly increases. This is not surprising since riblets lose their effectiveness on form drag in separated region that occurs at high lift coefficients. The drag decomposition in the case of NLF control with and without riblets is discussed in what follows. In the case of NLF control the wide extension of laminar zone on the wing requires the adoption of the sensor based on pseudo dissipation, as described in [23], for viscous drag computation. Figs. 22 and 23 reports the breakdown of the drag in its components without and with riblets. In the same figure the near field drag is also plotted showing the presence of 8 spurious drag counts. The drag decomposition shows that, also in the case of NLF control, a wave drag component is correctly detected at α = 4deg where supersonic regions appear. However, differently from the case of fully turbulent flow, in this

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Fig. 18. Wing body: M ∞ = 0.64, Re ∞ = 18.2 × 106 , fully turbulent, h = 2 grid. Drag breakdown without riblets.

Fig. 16. Wing body: M ∞ = 0.64, Re ∞ = 18.2 × 106 , extrapolation). Bookkeeping of drag reduction.

α = 0◦ , C L = 0.5 (zero mesh

Fig. 19. Wing body: M ∞ = 0.64, Re ∞ = 18.2 × 106 , fully turbulent, h = 2 grid. Drag breakdown with riblets.

Fig. 17. Wing body: M ∞ = 0.64, Re ∞ = 18.2 × 106 , fully turbulent, h = 2 grid. Computed far-field drag and near field drag vs mesh size with riblets.

case the presence of riblets does not influence the wave drag because the shock wave is in the laminar zone (see Fig. 24). It is worth noting that the supersonic zone in the case of NLF control and fully turbulent flow with riblets is slightly wider with respect to fully turbulent case without riblets. Indeed, the computed wave drag in the case of NLF control (21 drag counts) is substantially the same computed in the case of fully turbulent flow with riblets (22 drag counts). Thus the effect of riblets on shock wave is similar to the effect due to the NLF control.

Fig. 20. Wing body: M ∞ = 0.64, Re ∞ = 18.2 × 106 , Fully turbulent, h = 2 grid. Viscous drag breakdown without riblets.

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Fig. 21. Wing body: M ∞ = 0.64, Re ∞ = 18.2 × 106 , fully turbulent, h = 2 grid. Viscous drag breakdown with riblets. Fig. 23. Wing body: M ∞ = 0.64, Re ∞ = 18.2 × 106 , Natural Laminar Flow, h = 2 grid. Drag breakdown with NLF and riblets.

Fig. 22. Wing body: M ∞ = 0.64, Re ∞ = 18.2 × 106 , Natural Laminar Flow, h = 2 grid. Drag breakdown with NLF and without riblets.

The lift-induced drag is not influenced by riblets: they act totally on viscous drag. The decomposition of viscous drag in friction and form drag is shown in Fig. 25 without riblets and in Fig. 26 with riblets. The reduction of form drag, evident also in this case, is lower with respect to fully turbulent case. The drag decomposition finally allows for updating Figs. 12 and 13 with the computed form drag reduction (Figs. 27, 28). The form drag reduction due to riblets in cruise condition is 13% without NLF control and 7% with NLF control. It is worth remark that the behaviour of the form drag reduction in 3D flow is similar to the computed and experimental total drag reduction curves shown in Fig. 1 in the case of airfoil flows. 6. Conclusions The analyses of the effect of riblets on a new wing-body configuration designed to have an extended laminar zone on the wing has been proposed. The bookkeeping of drag reduction shows that, also in the case of laminar flows, the adoption of riblets on the fuselage and turbulent part of the wing provide an important contribution to drag reduction.

Fig. 24. Wing section: M ∞ = 0.64, Re ∞ = 18.2 × 106 , α = 4◦ . Visualization of the shock wave at η = 0.27 wing section (supersonic zone in red). Up: NLF without riblets, middle: turbulent without riblets (no flow control), down: turbulent with riblets.

B. Mele et al. / Aerospace Science and Technology 98 (2020) 105714

Fig. 25. Wing body: M ∞ = 0.64, Re ∞ = 18.2 × 106 , Natural Laminar Flow, h = 2 grid. Viscous drag breakdown with NLF and without riblets.

Fig. 26. Wing body, M ∞ = 0.64, Re ∞ = 18.2 × 106 , Natural Laminar Flow, h = 2 grid. Viscous drag breakdown with NLF and riblets.

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Fig. 27. Wing body, M ∞ = 0.64, Re ∞ = 18.2 × 106 , fully turbulent, h = 2 grid. Drag reduction due to riblets vs angle of attack (optimum height distribution on wing and fuselage). Reference value in percentages is smooth condition.

Fig. 28. Wing body, M ∞ = 0.64, Re ∞ = 18.2 × 106 , NLF h = 2 grid. Drag reduction due to riblets vs angle of attack (optimum height distribution on wing and fuselage). Reference value in percentages is smooth condition.

Declaration of competing interest The effect of riblets on form drag has been discussed and for the first time the breakdown of drag in its physical contributions has been computed in 3D flows in the case of riblets installed. The analysis provides interesting details on the different kind of drag where riblets acts. It has been shown that the drag reduction by riblets is obtained not only on friction drag but also on form drag. It has been confirmed that there is no effect on lift-induced drag while the wave drag increases due to increased intensity of shock wave in presence of riblets. It has also been shown that the increase of wave drag due to riblets is comparable to the increase of wave drag due to NLF control. The net effect of riblets is positive, in terms of drag reduction, also in transonic flow. Indeed, friction drag reduction is substantially constant with the angle of attack and the slight increase of wave drag in transonic condition has a small impact on the total drag reduction. Nevertheless, the increase of shock intensity must be taken into account in the design of aircraft with riblets installed.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This research has been carried out within IRON project, funded by Clean Sky 2 Joint Undertaking under the European Union’s Horizon 2020 research and innovation program under Grant Agreement n. CS2-REG-GAM-2014-2015-01. The authors would like to thank Donato De Rosa from CIRA, the Italian Aerospace Research Center, who provided the mesh. References [1] A. Abbas, J. de Vicente, E. Valero, Aerodynamic technologies to improve aircraft performance, Aerosp. Sci. Technol. 28 (2013) 100–132.

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