An Investigation of the Aerodynamic Performance for a Fuel Saving Double Channel Wing Conﬁguration

energies

Article An Investigation of the Aerodynamic Performance for a Fuel Saving Double Channel Wing Conﬁguration

Hongbo Wang, Wenbiao Gan * and Daochun Li

Institute of Unmanned System, Beijing University of Aeronautics and Astronautics, Beijing 100191, China; [email protected] (H.W.); [email protected] (D.L.) * Correspondence: [email protected]

Received: 23 August 2019; Accepted: 26 September 2019; Published: 16 October 2019

Abstract: This paper presents a fuel saving double channel wing (FADCW) configuration for a propeller driven aircraft to reduce fuel consumption. In pursuit of this objective, FADCW configuration combines the tractor propeller layout and over-the-wing propeller layout. The basic idea is to improve the wing lift-to-drag ratio by taking advantage of the beneficial propeller influence on the wing. Based on a multi reference frame method solving Reynolds averaged Navier-Stokes equations, the contrastive study of this configuration and a traditional tractor propeller-wing layout is conducted. It is shown that the propeller slipstream in the tractor propeller configuration leads to a 10.28% reduction in the wing lift-to-drag ratio. With the same reference wing area and the propeller rotation speed; however, the FADCW configuration can reduce the wing drag by 10.41% and increase its lift-to-drag ratio by 13.29%, which results in a 20.15% reduction in the fuel consumption compared with the traditional tractor propeller configuration.

Keywords: fuel saving; drag reduction; lift-to-drag ratio; propeller; slipstream; double channel wing conﬁguration

1. Introduction The rapid development of the aviation industry has brought about huge fuel consumption. Since aircraft aerodynamic design is one of the key elements that have critical effect on fuel consumption, designing a fuel saving aircraft has always been an important goal for aircraft designers. For a low speed fixed wing aircraft, a propeller has been a widely used propulsion model for a long time because of its high propulsion efficiency. Among propeller driven aircraft, a tractor propeller configuration (TPC) is the most widely used one, which can be seen frequently on many transport aircraft and a lot of low speed unmanned aerial vehicles. In this configuration, the propeller is located in front of the wing; its high speed slipstream, washing the wing directly and strongly, affects the pressure distribution of the wing significantly and thus generates a considerable impact on the aircraft’s stability, maneuverability, range, fuel consumption, and so on. For distributed propeller driven aircraft, the aerodynamic interaction between propellers and the wing will be more complex and stronger because of the enlarged area of the wing immersed in the distributed propeller slipstreams. Take the Helios solar-powered UAV (Unmanned Aerial Vehicle) [1] for example, about 50% of the wing is directly affected by propeller slipstreams. In recent years, with the rise of the distributed electric propulsion (DEP) aircraft [2–4], the percent of the wing area submerged in the propeller slipstream has been almost 100%. Therefore, the fuel consumption for a propeller driven aircraft heavily depends on the aerodynamic performance of the propeller-wing interaction. The propeller-wing aerodynamic interference has drawn extensive attention for a long time. Many researchers have studied the aerodynamic behavior of the wing under the propeller interference.

Energies 2019, 12, 3911; doi:10.3390/en12203911 www.mdpi.com/journal/energies Energies 2019, 12, 3911 2 of 16

Experimental measurements tested by Makino and Nagai [5] revealed that the propeller slipstream can delay or eliminate the separation bubble on the wing surface and thereby increase the wing lift in a flow of low Reynolds number. A numerical simulation on the DEP aircraft conducted by Stoll et al. [6] indicated that distributed propeller slipstreams can augment the maximum lift coefficient of the wing to 5.2. Regarding the drag of a wing for a propeller driven aircraft, Kroo’s analyses [7] showed that the propeller-wing interaction can reduce the wing drag obviously. However, Fratello et al. [8] drew a contrary conclusion. Their experiment revealed that the wing drag with the propeller influence is five times larger than that of a clean wing. Through the wind tunnel test, Ma et al. [9] also found that the propeller increases the wing drag and decreases its lift-to-drag ratio considerably. Miranda and Brennan [10] studied a wingtip mounted propeller configuration using a vorticity model and they suggested that whether the propeller-wing interaction is beneficial will strongly depend on the propeller rotation direction and installation position. Therefore, the aerodynamic behavior of the wing, especially the variation of the drag, is very sensitive to the influence of the propeller slipstream; more attention should be paid to employing the favorable influence of the propeller on the wing and avoiding its disadvantageous impact as much as possible. In view of the important influence of the propeller on the wing, some authors [11–13] have made airfoil and wing shape optimizations considering the propeller interference to promote the aerodynamic performance of the wing and acquired many good results. However, these works mainly focused on the tractor propeller configurations, where only the influence of the slipstream behind the propeller disk was investigated; the potential favorable effects upstream of the propeller blade on the wing are rarely considered. The goal of the present work is to improve the aerodynamic behavior of the wing and thus reduce the fuel consumption of a propeller driven aircraft. The basic idea is to take advantage of the favorable effects at both sides of the propeller disk. The performances of a tractor propeller-wing configuration and an isolated propeller are analyzed firstly to investigate their aerodynamic behavior and flow characteristics using CFD (Computational Fluid Dynamics) method. Based on these analyses, a fuel saving double channel wing (FADCW) configuration is proposed and its aerodynamic characteristics are discussed in detail to validate the design idea.

2. Numerical Method A commercial software, ANSYS Fluent, solving Reynolds-averaged Navier-Stokes (RANS) equations, is used to conduct the complex simulation of the propeller-wing aerodynamic interaction. The turbulence model is selected as the k-ω shear stress transport (SST) model [14] with a low Reynolds number correction for all computations. Considering the rotation of the propeller, three kinds of simulation methods (i.e., an actuator disk method [15], a multiple reference frame (MRF) [16] method, and an unsteady sliding mesh [17] method) are often used to simulate the interference of a propeller or a fan. In the actuator disk method, the propeller is replaced with a thin disk so as to improve the computational efficiency. Although the unsteady sliding mesh method can simulate the propeller rotation and has a higher accuracy than that of the actuator disk method, it needs more computational costs when there are a lot of flight states needed to be simulated. In order to balance the requirements between the computational efficiency and accuracy, the MRF method with a lower computational cost and no geometry simplification is employed to solve the rotating field surrounding the propeller blade. The spatial discretization and the temporal discretization are accomplished by the second-order Roe flux-difference method and the implicit LU-SGS (Lower upper symmetric Gauss-Seidel) [18] method, respectively, for all the CFD computations. Due to the importance of an accurate solution of the propeller flow field to the investigation of the wing performance, two wind tunnel models (i.e., a ducted propeller and a two-blade rotor) are simulated and tested to validate the accuracy of the MRF method. Energies 2019, 12, x FOR PEER REVIEW 3 of 16

2. Numerical Method A commercial software, ANSYS Fluent, solving Reynolds‐averaged Navier‐Stokes (RANS) equations, is used to conduct the complex simulation of the propeller‐wing aerodynamic interaction. The turbulence model is selected as the k‐ shear stress transport (SST) model [14] with a low Reynolds number correction for all computations. Considering the rotation of the propeller, three kinds of simulation methods (i.e., an actuator disk method [15], a multiple reference frame (MRF) [16] method, and an unsteady sliding mesh [17] method) are often used to simulate the interference of a propeller or a fan. In the actuator disk method, the propeller is replaced with a thin disk so as to improve the computational efficiency. Although the unsteady sliding mesh method can simulate the propeller rotation and has a higher accuracy than that of the actuator disk method, it needs more computational costs when there are a lot of flight states needed to be simulated. In order to balance the requirements between the computational efficiency and accuracy, the MRF method with a lower computational cost and no geometry simplification is employed to solve the rotating field surrounding the propeller blade. The spatial discretization and the temporal discretization are accomplished by the second‐order Roe flux‐difference method and the implicit LU‐SGS (Lower upper symmetric Gauss‐Seidel) [18] method, respectively, for all the CFD computations. Due to the importance of an accurate solution of the propeller flow field to the investigation of Energies 2019, 12, 3911 3 of 16 the wing performance, two wind tunnel models (i.e., a ducted propeller and a two‐blade rotor) are simulated and tested to validate the accuracy of the MRF method. 2.1. Ducted Propeller 2.1. Ducted Propeller The three-bladeThe three–blade geometry geometry model model of of the the ducted ducted propellerpropeller (Langley (Langley Research Research Center, Center, Hampton, Hampton, VA, USA)VA, USA) is shown is shown in Figure in Figure1. The 1. The diameter diameter of of the the propeller propeller andand the the chord chord of of the the duct duct are are 0.381 0.381 and and 0.2620.262 m, respectively. m, respectively. At At a winda wind tunnel tunnel speed of of 30.48 30.48 m/s, m /thes, the tested tested Reynolds Reynolds number number based on based the on the ductduct chord chord is is 5 5 ×10 1055andand thethe testedtested propeller rotation rotation speed speed is isselected selected as 8000 as 8000 r/min. r/min. The Theother other × propeller-bladepropeller‐blade and ductand duct geometric geometric parameters parameters can can be be found found in [19]. [19].

Figure 1. Three-blade ducted propeller and its surface mesh.

Figure 1. Three‐blade ducted propeller and its surface mesh. For the convenience of simulating the interaction between the rotating propeller and the stationary duct, a structuredFor the convenience and unstructured of simulating hybrid gridthe interaction approach isbetween adopted the to rotating improve propeller the effi ciencyand the of the grid generation.stationary duct, Considering a structured the and highly unstructured twisted bladehybrid of grid the approach propeller, is theadopted rotating to improve domain the (i.e., a cylindricalefficiency enclosed of the grid field generation. surrounding Considering the propeller the highly blade) twisted is discretized blade of the by propeller, an unstructured the rotating mesh with 2.5domain million (i.e., grid a cylindrical cells. The enclosed stationary field domain surrounding containing the propeller the rest blade) of the is field discretized is discretized by an by 5 millionunstructured structured mesh grid with cells. 2.5 million An O-grid grid cells. topology The stationary is set around domain the containing duct and the the rest hub. of the A distancefield of 50 timesis discretized the chord by 5 ofmillion the ductstructured is used grid in cells. each An direction O ‐grid topology from the is ducted set around propeller the duct to and create the the stationaryhub. domain.A distance A of pressure 50 times far the field chord boundary of the duct condition is used in is each applied direction in the from boundary the ducted of the propeller stationary to create the stationary domain. A pressure far field boundary condition is applied in the boundary domain and a non-slip boundary condition is utilized on the surfaces of the duct, blade, and hub. of the stationary domain and a non–slip boundary condition is utilized on the surfaces of the duct, Two interfaces,blade, and wherehub. Two the interfaces, stationary where domain the andstationary the rotating domain domain and the share rotating the domain same boundary, share the are established (named as Interface-1 and Interface-2 in Figure1) to exchange the flow information by using an interpolation method. Table1 compares the propeller thrust coe fficients of the experimental data and the calculated results. Although there is a strong interference between the propeller blades and the duct, the results of the CFD method show good agreement with the experimental measurements. The deviation from the experiment has an increase when the angle of attack increases to 10◦ or 20◦. The reason for this change is that a separation phenomenon occurs in the flow field at a large angle of attack which reduces the accuracy of the CFD method.

Table 1. Comparison of the propeller thrust coeﬃcient between the experiment and CFD methods.

α/◦ Experiment CFD Method Error 0 0.1419 0.1486 4.75% 10 0.1363 0.1461 7.19% 20 0.1350 0.1457 7.93%

2.2. Two-Blade Rotor The Caradonna-Tung two-blade rotor (Ames Research Center, Moffett Field, CA, USA) [20] uses an NACA (National Advisory Committee for Aeronautics) 0012 profile and has an untwisted rectangular shape with an aspect ratio (span-to-chord ratio) of 6. The chord of the blade is 0.1905 m and the radius is 1.143 m. More detailed geometric parameters and experimental data can be found in [20]. In this section, a collective pitch angle of 8◦ and two tested rotation speeds (1750 and 2250 r/min) at Energies 2019, 12, 3911 4 of 16 a hover state are simulated to further evaluate the accuracy of the CFD method. The experimental static pressure is 103,027 Pa, temperature 289.75 K, and density 1.2389 kg/m3. The process of the grid generation is in accordance with the one from the ducted propeller. Table2 lists the rotor thrust coe fficients CT [21] of the experiment and CFD method at different rotation speeds. Three mesh densities are used to conduct the grid dependence study: a coarse grid of 3.7 million cells, a medium grid of 7.5 million cells (about 5 million cells in the stationary domain and 2.5 million cells in the rotating domain), and a fine grid of 15 million cells. Figure2 shows the convergence of the rotor thrust coefficients for different grid sizes. It is obvious that the calculated results are very close to the experimental data and the errors between them are acceptable. Figure3 presents the chordwise pressure distribution for two blade stations at a rotation speed of 1750 r/min. On the whole, the computed pressures fall close to the measurements and the small deviations between them could be caused by the uncertainty of the experiment [22] or the numerical simulation. It indicates that the MRF method has good accuracy in capturing the characteristics in a rotating field.

Table 2. Rotor thrust coeﬃcients CT at diﬀerent rotation speeds.

CFD Method Rotation Speed Experiment Coarse Grid Medium Grid Fine Grid 1750 r/min 0.00455 0.004857 0.004737 0.004692 Energies 20192250, 12, rx/ minFOR PEER REVIEW 0.00462 0.004998 0.004910 0.004870 5 of 16 Energies 2019, 12, x FOR PEER REVIEW 5 of 16

Figure 2. Convergence of the rotor thrust coefficient for different mesh densities (  = 1750r /min ). FigureFigure 2. Convergence 2. Convergence of of the the rotor rotor thrust thrust coe coefficientﬃcient for for different diﬀerent mesh mesh densities densities (  (=Ω 1750= 1750r /min r/).min ).

(a) (b) (a) (b) FigureFigure 3. Chordwise 3. Chordwise pressure pressure distribution distribution on on the the rotor rotor bladeblade at a a rotation rotation speed speed of of 1750 1750 r/min: r/min: (a) (r/Ra) r/R = Figure 3. Chordwise pressure distribution on the rotor blade at a rotation speed of 1750 r/min: (a) r/R 0.68;= (b 0.68;) r/R (b=) 0.89.r/R = 0.89. = 0.68; (b) r/R = 0.89. 3. Configurations 3. Configurations 3.1. Tractor Propeller‐Wing Interaction 3.1. Tractor Propeller‐Wing Interaction For a tractor propeller driven aircraft, a portion of the wing is submerged in the propeller slipstream,For a tractorand its flowpropeller characteristic driven aircraft, will be differenta portion from of thethat wing of the is wing submerged outside ofin thethe slipstream propeller becauseslipstream, of the and strong its flow propeller characteristic interference. will be Indifferent this section, from thata tractor of the propeller wing outside configuration of the slipstream (TPC), asbecause depicted of the in Figurestrong propeller4, is analyzed interference. to investigate In this the section, basic aaerodynamic tractor propeller characteristic configuration of the (TPC), wing influencedas depicted by in theFigure propeller. 4, is analyzed The relevant to investigate calculating the parametersbasic aerodynamic are as follow: characteristic Reynolds of thenumber, wing influencedRe 4.88 10 by5 , theMach propeller. number The, Ma relevant = 0.1017, calculating angle of attack parameters =2o . Theare wingas follow: has a Reynoldschord of 2.6number, m, an 5 o aspectRe 4.88 ratio 10 (wing, Mach span number to chord , Ma ratio) = 0.1017, of 2, angle and ofan attack incidence =2 angle. The ofwing 4°. hasThe apropeller chord of radius2.6 m, anis 0.4125aspect m.ratio The (wing process span of to the chord mesh ratio) generation of 2, and and an theincidence types ofangle the boundaryof 4°. The conditionspropeller radius for this is configuration0.4125 m. The are process the same of the as thosemesh describedgeneration in andSection the 2.types A medium of the boundarygird size (i.e., conditions about 5 formillion this gridconfiguration cells in the are stationary the same domainas those and described 2.5 million in Section grid cells 2. A in medium the rotating gird sizedomain) (i.e., aboutis used 5 formillion this tractorgrid cells propeller in the stationaryconfiguration domain to conduct and 2.5 the million simulations. grid cells in the rotating domain) is used for this tractorIn propellerFigure 4a, configuration the propeller tohas conduct a clockwise the simulations. rotating direction and its rotation speed is chosen to be 4400In Figure r/min 4a,so thatthe propeller the propeller has a clockwisethrust equals rotating the dragdirection of the and wing. its rotation For the speed convenience is chosen ofto description,be 4400 r/min the so axial that and the vertical propeller spacings thrust betweenequals the the dragpropeller of the centerline wing. For and the the convenience wing leading of edgedescription, are nondimensionalized the axial and vertical by spacings propeller between radius the R propeller and denoted centerline as andX theR wingand leadingZ R , respectively.edge are nondimensionalized It should be noted thatby propelleronly the influenceradius Rof andthe verticaldenoted installation as X Rposition and ofZ theR , propellerrespectively. is considered It should bein thisnoted section. that only The thepropeller influence chordwise of the verticaland spanwise installation positions position are kept of the as constantspropeller andis considered located at in thisXR section.1.0 and Theyb propeller=0, respectively. chordwise and spanwise positions are kept as constants and located at XR 1.0 and yb=0, respectively.

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3. Conﬁgurations

3.1. Tractor Propeller-Wing Interaction For a tractor propeller driven aircraft, a portion of the wing is submerged in the propeller slipstream, and its flow characteristic will be different from that of the wing outside of the slipstream because of the strong propeller interference. In this section, a tractor propeller configuration (TPC), as depicted in Figure4, is analyzed to investigate the basic aerodynamic characteristic of the wing influenced by the propeller. The relevant calculating parameters are as follow: Reynolds number, Re = 4.88 105, Mach number, Ma = 0.1017, angle of attack α = 2 . The wing has a chord of 2.6 m, × ◦ an aspect ratio (wing span to chord ratio) of 2, and an incidence angle of 4◦. The propeller radius is 0.4125 m. The process of the mesh generation and the types of the boundary conditions for this configuration are the same as those described in Section2. A medium gird size (i.e., about 5 million grid cellsEnergies in 2019 the, 12 stationary, x FOR PEER domain REVIEW and 2.5 million grid cells in the rotating domain) is used6 of for 16 this tractor propeller configuration to conduct the simulations.

(a) (b)

FigureFigure 4. A 4. tractor A tractor propeller-wing propeller‐wing conﬁguration: configuration: ( (aa)) Oblique Oblique view; view; (b) ( bside) side view. view.

In FigureFigure4a, 5 thepresents propeller the variation has a clockwise of lift and rotatingdrag coefficients direction of the and wing its rotation for different speed propeller is chosen to bepositions. 4400 r/min In soFigure that 5a, the the propeller propeller thrust slipstream equals causes the a drag slight of increase the wing. of the For wing the lift convenience coefficient of Z R Z R description,within a the range axial of and vertical= 0 – 1.5 spacings and an obvious between augmentation the propeller of centerlinethe drag for and all the wing. The leadingmaximal edge increments of CL and CD occur at Z R = 0.75, where C = 1.1% and C = 18.39% compared are nondimensionalized by propeller radius R and denotedL asmax∆X/R and ∆ZD/maxR, respectively. It should with a clean wing with the same reference area. Due to the larger magnitude of C than that be noted that only the influence of the vertical installation position of the propeller isD considered in C Z R this section.of L , the The lift–to–drag propeller ratio chordwise of the wing and spanwiseis decreases positions for all are kept and asthe constants maximal reduction and located is at ∆X/Robserved= 1.0 andto bey by/b 13.33%= 0, respectively. (see Figure 5b). − Figure5 presents the variation of lift and drag coe fficients of the wing for different propeller positions. In Figure5a, the propeller slipstream causes a slight increase of the wing lift coe fficient within a range of ∆Z/R = 0 1.5 and an obvious augmentation of the drag for all ∆Z/R. The maximal − increments of CL and CD occur at ∆Z/R = 0.75, where ∆CLmax= 1.1% and ∆CDmax = 18.39% compared with a clean wing with the same reference area. Due to the larger magnitude of ∆CD than that of ∆CL, the lift-to-drag ratio of the wing is decreases for all ∆Z/R and the maximal reduction is observed to be by 13.33% (see Figure5b). The propeller injects energy into the free stream through its rotation and causes an apparent axial acceleration on the free stream, which is helpful to augment the lift of the wing. The obvious increase of the wing drag can be attributed to the increased pressure drag and skin friction drag. When the slipstream encounters the wing, the wing’s blocking effect reduces the air speed and causes the total pressure of the stagnation point(a at) the wing leading edge to be greater(b) than that of a clean wing, and finally leadsFigure to an5. Variations increase of of lift the and pressure drag coefficients drag of of the wing wing. for Indifferent addition, Z R the: (a) propellerLift and drag can easily o cause a turbulencecoefficients boundary versus Z layerR ; (b) [lift23‐]to for‐drag the ratio portion versus of  theZ R wing. (Ma = immersed 0.1017, =2 in,  the= 4400 slipstream,r min , which will have anmedium impact grid). on the skin friction drag C f of the wing. Figure6 compares the distribution of C f of the clean wing and the tractor propeller configuration under the same calculation conditions. The comparisonThe propeller demonstrates injects energy that theinto increasedthe free streamC f of through the wing its rotation mainly and comes causes from an theapparent propeller slipstreamaxial acceleration region (between on the thefree twostream, red which dashed is helpful lines in to Figure augment6b). the In lift this of region,the wing. on The one obvious hand, the increase of the wing drag can be attributed to the increased pressure drag and skin friction drag. When the slipstream encounters the wing, the wing’s blocking effect reduces the air speed and causes the total pressure of the stagnation point at the wing leading edge to be greater than that of a clean wing, and finally leads to an increase of the pressure drag of the wing. In addition, the propeller can easily cause a turbulence boundary layer [23] for the portion of the wing immersed in

the slipstream, which will have an impact on the skin friction drag C f of the wing. Figure 6

compares the distribution of C f of the clean wing and the tractor propeller configuration under the

same calculation conditions. The comparison demonstrates that the increased C f of the wing mainly comes from the propeller slipstream region (between the two red dashed lines in Figure 6b). In this region, on one hand, the normal velocity gradient of the air near the surface of the wing is enhanced by the axial acceleration action of the propeller slipstream; on the other hand, a lot of complex

Energies 2019, 12, x FOR PEER REVIEW 6 of 16

(a) (b)

Energies 2019, 12, 3911Figure 4. A tractor propeller‐wing configuration: (a) Oblique view; (b) side view. 6 of 16

Figure 5 presents the variation of lift and drag coefficients of the wing for different propeller normalpositions. velocity In gradientFigure 5a, of the the propeller air near slipstream the surface causes of the a slight wing increase is enhanced of the by wing the lift axial coefficient acceleration actionwithin of the a range propeller of Z slipstream;R = 0 – 1.5 and on an the obvious other hand,augmentation a lot of of complex the drag high-levelfor all Z R turbulence. The maximal ﬂow is generated in this region caused by the propeller rotation. It is these two factors that cause an increase increments of CL and CD occur at Z R = 0.75, where CL max = 1.1% and CDmax = 18.39% compared in thewith skin a frictionclean wing drag with of the the wing. same reference Since the area. main Due portion to the of larger the wing magnitude drag is of the  skinC than friction that drag, D its reduction through a ﬂow control approach [24] or an outstanding aerodynamic design should draw of CL , the lift–to–drag ratio of the wing is decreases for all Z R and the maximal reduction is enoughobserved attention. to be by 13.33% (see Figure 5b).

Energies 2019, 12, x FOR PEER REVIEW 7 of 16 (a) (b) high‐level turbulence flow is generated in this region caused by the propeller rotation. It is these two Figure 5. Variations of lift and drag coefficients of the wing for different Z R : (a) Lift and drag Figurefactors that 5. Variations cause an increase of lift and in the drag skin coe frictionfficients drag of theof the wing wing. for Since different the main∆Z/ Rportion:(a) Lift of andthe wing drag coefficients versus Z R ; (b) lift‐to‐drag ratio versus Z R (Ma = 0.1017, =2o ,  = 4400r min , coedragffi iscients the skin versus friction∆Z/ Rdrag,;(b ) lift-to-dragits reduction ratio through versus a ∆flowZ/R control.(. Ma = approach0.1017, α [24]= 2 ◦or, Ωan= outstanding4400 r/min , mediumaerodynamicmedium grid). grid). design should draw enough attention.

The propeller injects energy into the free stream through its rotation and causes an apparent axial acceleration on the free stream, which is helpful to augment the lift of the wing. The obvious increase of the wing drag can be attributed to the increased pressure drag and skin friction drag. When the slipstream encounters the wing, the wing’s blocking effect reduces the air speed and causes the total pressure of the stagnation point at the wing leading edge to be greater than that of a clean wing, and finally leads to an increase of the pressure drag of the wing. In addition, the propeller can easily cause a turbulence boundary layer [23] for the portion of the wing immersed in

the slipstream, which will have an impact on the skin friction drag C f of the wing. Figure 6

compares the distribution of C f of the clean wing and the tractor propeller configuration under the

same calculation conditions. The comparison demonstrates that the increased C f of the wing mainly comes from the propeller slipstream(a) region (between the two red dashed(b) lines in Figure 6b). In this region,FigureFigure 6.onComparison one 6. Comparison hand, the of normal theof the skin skin velocity friction friction draggradient drag coe coefficientﬃ ofcient the air distribution distribution near the surface betweenbetween of the the the clean clean wing wing wing is enhanced and and the by the axial accelerationC action of the propellerC slipstream; on the other hand,=2o  a= lot 4400 ofr complex min TPC:the (a) TPC:C f on (a) the f cleanon the wing;clean wing; (b) C (fb)in TPCf in TPC conﬁguration. configuration. (Ma (Ma= = 0.1017, α = ,2◦, Ω = 4400 r,/ min, mediummedium grid). grid).

ExceptExcept for thefor the direct direct influence influence of of the the slipstream, slipstream, the the propeller propeller vertical vertical installation installation position position also also has ahas non-ignorable a non–ignorable effect effect on on the the wing. wing. With With the the variationvariation of of∆ZZR/,R the, the ratio ratio between between the slipstreams the slipstreams flowingflowing through through the the top top and and bottom bottom surface surface of of thethe wing will will be be changed. changed. When WhenZ ∆RZ has/R ahas negative a negative value,value, the area the area strongly strongly aff ectedaffected by by the the propeller propeller is mainly the the bottom bottom surface surface of the of thewing, wing, where where the the axialaxial acceleration acceleration eff ecteffect of of the the propeller propeller slipstream slipstream decreases decreases the the static static pressure pressure of the of air the and air hence and hence causescauses a reduction a reduction in the in wing the wing lift. Oncelift. Once the propellerthe propeller is moved is moved upward upward and and∆Z /RZ hasR has a small a small positive value,positive the acceleration value, the acceleration effect makes effect the makes static the pressure static pressure on the top on the surface top surface of the of wing the wing more more negative, whichnegative, means thatwhich the means suction that force the suction on this surfaceforce on isthis enhanced surface andis enhanced more lift and can more be obtained. lift can be When obtained. When Z R is further increased to be higher than 0.75, the beneficial influence of the ∆Z/R is further increased to be higher than 0.75, the beneficial influence of the propeller on the wing is propeller on the wing is weakened because of a far distance between them. As a result, the values of weakened because of a far distance between them. As a result, the values of the lift and drag of the the lift and drag of the wing gradually return to those of a clean wing without the slipstream wing gradually return to those of a clean wing without the slipstream interference. interference. In orderIn order to demonstrate to demonstrate further further the propellerthe propeller influence influence on theon wing,the wing, Figure Figure7 presents 7 presents the pressurethe distributionpressure along distribution the wing along span the atwing diff spanerent at chordwise different chordwise positions positions of x/c. It of should x/c. It should be noted be noted that y /b = that y/b = −1 and y/b = 1 in this figure represent the left and right wing tips, respectively, and the propeller is located at a spanwise position of y/b = 0.

(a) (b)

Energies 2019, 12, x FOR PEER REVIEW 7 of 16

high‐level turbulence flow is generated in this region caused by the propeller rotation. It is these two factors that cause an increase in the skin friction drag of the wing. Since the main portion of the wing drag is the skin friction drag, its reduction through a flow control approach [24] or an outstanding aerodynamic design should draw enough attention.

(a) (b)

Figure 6. Comparison of the skin friction drag coefficient distribution between the clean wing and o the TPC: (a) C f on the clean wing; (b) C f in TPC configuration. (Ma = 0.1017, =2 ,  = 4400r min , medium grid).

Except for the direct influence of the slipstream, the propeller vertical installation position also has a non–ignorable effect on the wing. With the variation of Z R , the ratio between the slipstreams flowing through the top and bottom surface of the wing will be changed. When Z R has a negative value, the area strongly affected by the propeller is mainly the bottom surface of the wing, where the axial acceleration effect of the propeller slipstream decreases the static pressure of the air and hence causes a reduction in the wing lift. Once the propeller is moved upward and Z R has a small positive value, the acceleration effect makes the static pressure on the top surface of the wing more negative, which means that the suction force on this surface is enhanced and more lift can be obtained. When Z R is further increased to be higher than 0.75, the beneficial influence of the propeller on the wing is weakened because of a far distance between them. As a result, the values of the lift and drag of the wing gradually return to those of a clean wing without the slipstream Energies 2019 12 interference., , 3911 7 of 16 In order to demonstrate further the propeller influence on the wing, Figure 7 presents the pressure distribution along the wing span at different chordwise positions of x/c. It should be noted 1 and y/b = 1 in this ﬁgure represent the left and right wing tips, respectively, and the propeller is − that y/b = −1 and y/b = 1 in this figure represent the left and right wing tips, respectively, and the located at a spanwise position of y/b = 0. propeller is located at a spanwise position of y/b = 0.

(a) (b)

Figure 7. Spanwise pressure distribution of the wing: (a) x/c = 0.25; (b) x/c = 0.5. (Ma = 0.1017, α = 2◦, Ω = 4400 r/min, medium grid).

Since a chordwise position of x/c = 0.25 (see Figure7a) on the wing is very close to the propeller blade, an apparent lift enhancing effect caused by the slipstream acceleration action occurs at the segment of the wing within a scope of the propeller diameter when ∆Z/R is raised. For the portion of the wing outside of the propeller diameter; however, the pressure coefficient CP is almost identical to that of the clean wing. This result demonstrates that the influenced range on the wing is very limited; its width is slightly larger than the propeller diameter Dp. In addition, the curve trends in the scope of the propeller diameter for ∆Z/R = 0.5 and 0.5 show that an asymmetry pressure distribution − occurs at two sides of the propeller axis (y/b = 0). The reason for this phenomenon is the upwash and downwash effects induced by the corresponding up-going and down-going propeller blades. These two effects increase and decrease the local effective angle of attack of the wing, respectively, and then result in the difference at the symmetry locations with respect to the propeller axis. The locations of upwash and downwash regions depend on the propeller rotation direction, and the final shape of the spanwise pressure distribution curve will be determined simultaneously by the propeller mounted position and its rotation direction. When the propeller slipstream flows downstream, its kinetic energy decreases rapidly due to the viscous dissipation of the air. As a result, the axial acceleration action is correspondingly weakened. Meanwhile, the presence of the wing divides the slipstream into two parts, and it suppresses the circumferential rotation of the slipstream obviously, which causes the upwash and downwash effects also to be weakened. Due to the diminished influence of the propeller, the lift increment at x/c = 0.5 is less than that at x/c = 0.25, and the curve of the spanwise pressure distribution is restored basically to be symmetry.

3.2. Fuel Saving Double Channel Wing Configuration The results presented in Figure5 indicate that the tractor propeller slipstream increases the lift and drag of the wing and results in a considerable reduction in its lift-to-drag ratio. Moreover, the variation of the vertical installation position of the propeller can affect this aerodynamic behavior of the wing significantly. For some values of ∆Z/R, the propeller slipstream will be helpful for the wing to reduce its drag, despite the fact that the wing drag affected by the propeller is larger than that of a clean wing. Based on the above results, there is a possibility that the wing drag could be further reduced to a magnitude which is smaller than that of the clean wing and then the lift-to-drag ratio is improved apparently if the propeller is located at a reasonable position. In order to realize Energies 2019, 12, x FOR PEER REVIEW 8 of 16

Figure 7. Spanwise pressure distribution of the wing: (a) x/c = 0.25; (b) x/c = 0.5. (Ma = 0.1017,=2o ,  = 4400r min , medium grid).

Since a chordwise position of x/c = 0.25 (see Figure 7a) on the wing is very close to the propeller blade, an apparent lift enhancing effect caused by the slipstream acceleration action occurs at the segment of the wing within a scope of the propeller diameter when Z R is raised. For the portion

of the wing outside of the propeller diameter; however, the pressure coefficient CP is almost identical to that of the clean wing. This result demonstrates that the influenced range on the wing is very limited; its width is slightly larger than the propeller diameter Dp. In addition, the curve trends in the scope of the propeller diameter for Z R = −0.5 and 0.5 show that an asymmetry pressure distribution occurs at two sides of the propeller axis (y/b = 0). The reason for this phenomenon is the upwash and downwash effects induced by the corresponding up–going and down–going propeller blades. These two effects increase and decrease the local effective angle of attack of the wing, respectively, and then result in the difference at the symmetry locations with respect to the propeller axis. The locations of upwash and downwash regions depend on the propeller rotation direction, and the final shape of the spanwise pressure distribution curve will be determined simultaneously by the propeller mounted position and its rotation direction. When the propeller slipstream flows downstream, its kinetic energy decreases rapidly due to the viscous dissipation of the air. As a result, the axial acceleration action is correspondingly weakened. Meanwhile, the presence of the wing divides the slipstream into two parts, and it suppresses the circumferential rotation of the slipstream obviously, which causes the upwash and downwash effects also to be weakened. Due to the diminished influence of the propeller, the lift increment at x/c = 0.5 is less than that at x/c = 0.25, and the curve of the spanwise pressure distribution is restored basically to be symmetry.

3.2. Fuel Saving Double Channel Wing Configuration The results presented in Figure 5 indicate that the tractor propeller slipstream increases the lift and drag of the wing and results in a considerable reduction in its lift–‐to–drag ratio. Moreover, the variation of the vertical installation position of the propeller can affect this aerodynamic behavior of the wing significantly. For some values of Z R , the propeller slipstream will be helpful for the wing to reduce its drag, despite the fact that the wing drag affected by the propeller is larger than Energiesthat2019 of ,a12 clean, 3911 wing. Based on the above results, there is a possibility that the wing drag could be 8 of 16 further reduced to a magnitude which is smaller than that of the clean wing and then the lift–to–drag ratioEnergies is improved2019, 12, x FOR apparently PEER REVIEW if the propeller is located at a reasonable position. In order to realize9 of 16 thisthis possibility, possibility, in in this this section, section, an an analysis analysis of of an an isolated isolated propeller propeller (see (see Figure Figure 8) flow8) ﬂow characteristic characteristic is is 5 necessarynecessarychord andin Figureand important. important. 4 is unchanged (i.e., Re 4.88 10 ). A medium grid size of 7.5 million is used again

for the simulation of the propeller. In this figure, X P R and ZP R are the dimensionless axial

and radial positions, respectively, VX is an increment of the local axial velocity and V is the free stream velocity. It indicates that the induced velocity distributions upstream and downstream of the propeller disk are quite different from each other. In Figure 9a, a low pressure region is generated in front of this disk by the propeller rotation and it produces a suction action on the free stream. The closer to the propeller disk, the more dimensionless increment of the axial speed, denoted as VV in X  Figure 9, can be obtained. Take the case of ZR 0 as an example, the VVX  rapidly increases from 0.015 to 0.16 when X R changes from a value of −4.0 to −1.0. Obviously, this suction action

can be apparently enhanced as X R approaches zero. Compared withFigure theFigure result 8. 8. AxialAxial in Figure and radial radial9a, Figure positions positions 9b ofdemonstrates ofan anisolated isolated propeller. that propeller. the axial acceleration effect of the slipstream behind the propeller is stronger than that induced by the suction effect. TheThe induced induced velocity velocity distribution distribution of anof isolatedan isolated propeller propeller is described is described in Figure in Figure9, whose 9, whose calculation For XR 1.0 , the maximal increment of the air speed is about four times that at XR=1.0. parameterscalculation are parameters as follows: are Rotation as follows: speed, RotationΩ =speed,4400 r/=min 4400, propeller r/min , propeller radius, radius,R = 0.4125R = 0.4125 m, Mach Although the propeller slipstream accelerated the free stream considerably, the scope of the m, Mach number, Ma = 0.1017, angle= of attack   0 , the Reynolds number based on the wing number,inducingMa = action0.1017, caused angle by of attackthe slipstreamα 0◦, theis very Reynolds limited. number Taking based the result on the of wingXR chord=1.0 inas Figurean 4 5 is unchanged (i.e., Re = 4.88 10 ). A medium grid size of 7.5 million is used again for the simulation example again, the maximal× radial distance from the propeller axis affected by the slipstream is of theslightly propeller. larger In than this ﬁgure,the propeller∆XP/ Rradius.and ∆ ForZP /theR are case the of dimensionless XR=1.0 depicted axial and in radial Figure positions, 9a; respectively, ∆VX is an increment of the local axial velocity and V is the free stream velocity. however, this radial distance can be three times the propeller radius.∞

(a) (b)

FigureFigure 9. Distributions 9. Distributions of of the the propeller propeller induced induced velocity for for different diﬀerent locations: locations: (a) Upstream (a) Upstream of the of the propeller disk; (b) downstream of the propeller disk. (Ma = 0.1017,   0 ,  = 4400 r/min , propeller disk; (b) downstream of the propeller disk. (Ma = 0.1017, α = 0◦, Ω = 4400 r/min, medium grid size).medium grid size).

It indicatesSo the slipstream that the induced behind the velocity propeller distributions disk has a stronger upstream action and downstreamthan the suction of effect the propeller in front disk are quiteof the di propellerfferent from in accelerating each other. the In free Figure stream.9a, a However, low pressure the latter region can is generatedgenerate a larger in front region of this to disk by theincrease propeller the air rotation velocity. and Considering it produces their a suction respective action advantages, on the free perhaps stream. both The beneficial closer to effects the propeller can be used simultaneously to reduce the wing drag and increase its lift–to–drag ratio. In order to realize disk, the more dimensionless increment of the axial speed, denoted as ∆VX/V in Figure9, can be this goal, a new configuration is needed. ∞ obtained. Take the case of ∆Z/R = 0 as an example, the ∆VX/V rapidly increases from 0.015 to 0.16 For the purpose of utilizing the suction effect ahead of the∞ propeller, it is better that the when ∆X/R changes from a value of 4.0 to 1.0. Obviously, this suction action can be apparently propeller is placed above the wing, −which is− called over–the–wing (OTW) propeller configuration enhanced[25–27]. as ∆TheX/ Rexperimentalapproaches result zero. demonstrates that the OTW configuration has an excellent Comparedadvantage of with reducing the result the wing in Figure drag 9througha, Figure the9b propeller demonstrates blade suction that the compared axial acceleration with a tractor e ffect of the slipstreampropeller arrangement, behind the propeller while its lift is stronger enhancing than capability that induced is slightly by theweaker suction than e theffect. latter. For In∆ Xorder/R = 1.0, the maximalto make incrementgood use of of the the potential air speed favorable is about effects four times occurring that at at∆ bothX/R sides= 1.0of the. Although propeller the disk propeller to − slipstreaminfluence accelerated the wing, the combining free stream the advantages considerably, of theTPC scope and OTW of the into inducing a new actionconfiguration caused is by the slipstreamprobably is veryan effective limited. way. Taking the result of ∆X/R = 1.0 as an example again, the maximal radial distance from the propeller axis affected by the slipstream is slightly larger than the propeller radius. For the case of ∆X/R = 1.0 depicted in Figure9a; however, this radial distance can be three times the − propeller radius. Energies 2019, 12, 3911 9 of 16

So the slipstream behind the propeller disk has a stronger action than the suction effect in front of theEnergies propeller 2019, 12 in, x FOR accelerating PEER REVIEW the free stream. However, the latter can generate a larger10 regionof 16 to increase the air velocity. Considering their respective advantages, perhaps both beneficial effects can be used simultaneouslyIn order to maximize to reduce the suction the wing strength drag of and the increasepropeller, its the lift-to-drag induced velocity ratio. distribution In order to in realize this goal,Figure a new9a needs configuration to be analyzed is needed. again. For XR=1.0, it is seen that there is a rapid increment of Forthe free–stream the purpose velocity of utilizing once theZR suction<1.5, and effect the ahead magnitude of the is propeller, very close it to is the better maximum that the when propeller is placedZR above<0.5. theTherefore, wing, whichit is necessary is called to over-the-wing make the propeller (OTW) as close propeller as possible configuration to the wing [25 in– 27the]. The experimentalvertical direction result demonstrates to enforce the thatsuction the effect OTW to configuration be effective. A has preferable an excellent way is advantage to set the vertical of reducing the wingdistance drag between through them the to propeller be smaller blade than 1.0 suction R. According compared to the with demands a tractor described propeller above, arrangement, a fuel whilesaving its lift double enhancing channel capability wing (FADCW) is slightly configuration weaker than is proposed the latter. and In is ordershown to in make Figure good 10. use of the In this configuration, the portion of the main wing under the propeller is designed into an potential favorable effects occurring at both sides of the propeller disk to influence the wing, combining arched shape [28,29] to meet the requirement of a low propeller installation position in the vertical the advantages of TPC and OTW into a new configuration is probably an effective way. direction. The circle center of the arc coincides with the propeller axis. In addition, the aided wing is Inalso order designed to maximize into the shape the suctionof a circular strength arc with of the the same propeller, radius theas the induced main wing velocity in order distribution to avoid in Figure9a needs to be analyzed again. For ∆X/R = 1.0, it is seen that there is a rapid increment of the center of the propeller being lower than the leading− edge of the aided wing. A concept of the free-streamembedding velocitydepth is adopted once ∆Z for/R the< 1 convenience.5, and the magnitudeof describing is the very bending close todegree the maximumof the arced when ∆Z/Rwing.< 0.5 It. is Therefore, defined as the it is vertical necessary distance to make between the point propeller A (a midpoint) as close and as possible point B shown to the in wing Figure in the vertical10, directionand is dimensionless to enforce with the the suction propeller effect radius to be (denoted effective. as  AH preferableR ). In this paper, way is the to influence set the vertical of distancethe embedding between them depth to beH R smalleris not discussed than 1.0 Rhere. According and only tothe the impact demands of HR described=0.3 is above, used to a fuel savingcarry double out the channel analysis wing of the (FADCW) aerodynamic configuration characteristic is for proposed the FADCW and isconfiguration. shown in Figure 10.

Figure 10. Fuel saving double channel wing configuration. Figure 10. Fuel saving double channel wing configuration. In this configuration, the portion of the main wing under the propeller is designed into an arched shape [28,It29 should] to meet be noted the requirement that the chord of alength low propellerof the aided installation wing is scaled position to 1/4 in of the that vertical depicted direction. in The circleFigure center 4 to ofavoid the arca significant coincides withincrease the propellerof the wing axis. drag In addition,caused by the the aided propeller wing isslipstream. also designed into theMeanwhile, shape of the a circular main wing arc chord with theis reduced same radiusto 3/4 C as to the ensure main that wing the intotal order reference to avoid area theof these center of the propellertwo wings being is equal lower to the than wing the in leading the TPC edge configuration. of the aided The wing.propeller A conceptis located of at embedding 70% of the main depth is wing chord in order to increase the wing lift as much as possible on the premise of a smaller drag adopted for the convenience of describing the bending degree of the arced wing. It is defined as the than the clean wing. The vertical distance between the trailing edges of these two wings is selected vertical distance between point A (a midpoint) and point B shown in Figure 10, and is dimensionless as 30% of the chord of the main wing. The Reynolds number based on the wing chord in Figure 4 is withstill the propellerRe 4.88 radius105 and (denoted the Mach asnumber∆H/ Ris). Ma In = this0.1017. paper, the influence of the embedding depth ∆H/R is notAn discussedaircraft’s fuel here consumption and only the depends impact of heavily∆H/R on= 0.3its isaerodynamic used to carry design. out the For analysis a long of the aerodynamicendurance characteristic cruise, the lift–to–drag for the FADCW ratio configuration.is a critical parameter to measure the aerodynamic Itperformance should be of noted an aircraft. that the Hence chord it closely length relates of the to the aided fuel wing consumption. is scaled In to order 1/4 ofto measure that depicted and in Figurecompare4 to avoid quantitatively a significant the increase fuel saving of the ability wing between drag caused the TPC by and the FADCW propeller configurations slipstream. Meanwhile,used in the mainthis paper, wing chorda relationship is reduced between to 3/4 the C tofuel ensure consumption that the and total the reference lift–to–drag area ratio of these is necessary. two wings is equalAssume to the wing that these in the two TPC configurations configuration. fly at The the propeller same altitude is located and weight, at 70% so of the the fuel main consumption wing chord in (FC) ratio for them will be proportional to the ratio of their cruise power, which can be expressed as order to increase the wing lift as much as possible on the premise of a smaller drag than the clean wing. follows: The vertical distance between the trailing edges of these two wings is selected as 30% of the chord of FC T V 5 the main wing. The Reynolds number based onTPC the wing chord TPC in Figure4 is still Re = 4.88 10 and  , ×(1) the Mach number is Ma = 0.1017. FCFADCW T V FADCW An aircraft’s fuel consumption depends heavily on its aerodynamic design. For a long endurance cruise, the lift-to-drag ratio is a critical parameter to measure the aerodynamic performance of an aircraft.

Energies 2019, 12, 3911 10 of 16 Energies 2019, 12, x FOR PEER REVIEW 11 of 16

Hencewhere it closely FC represents relates to the the fuel fuel consumption, consumption. T and In order V are to the measure thrust and and cruise compare speed quantitatively at a cruise state, the fuel savingrespectively. ability between the TPC and FADCW configurations used in this paper, a relationship between the fuel consumptionSince the thrust and at a the cruise lift-to-drag state should ratio be is equal necessary. to the drag Assume of an thataircraft these in order two configurationsto maintain a fly steady flight, the thrust T in Equation (1) can be replaced by: at the same altitude and weight, so the fuel consumption (FC) ratio for them will be proportional to the ratio of their cruise power, which can be expressedW as follows: T  , (2) CCL / D (FC)TPC (T V)TPC where W is the weight of the aircraft, CC/ is= the lift‐·to‐drag ratio., (1) (FC) L D (T V) In addition, with the same weightFADCW and reference· wingFADCW area, the relation between the cruise C wherespeedFC Vrepresents and the lift the coefficient fuel consumption, L for TPC andT andPADCWV are configurations the thrust can and be cruise expressed speed as: at a cruise state, respectively. C VTPC LTPC Since the thrust at a cruise state should be equal to the. drag of an aircraft in order to maintain(3) a VCFADCW L FADCW steady flight, the thrust T in Equation (1) can be replaced by: Substituting Equations (2) and (3) into Equation (1), the expression of the relationship between W the fuel consumption and the lift‐to‐drag ratioT = is: (2) CL/CD 3 2 CCLD where W is the weight of the aircraft, CFCL/CD is the lift-to-drag ratio. FADCW TPC . (4) In addition, with the same weight andFC reference3 wing area, the relation between the cruise speed TPC 2 CCLD V and the lift coefficient CL for TPC and PADCW configurations can be expressed as: FADCW

Equation (4) indicates that the fuel consumptionr ratio between TPC and FADCW VTPC CLTPC configurations is inversely proportional to their= ratio of CC/ ., which means that an aircraft with (3) VFADCW CLFADCWL D a high lift–to–drag ratio ( CCL / D ) has a low fuel consumption at the cruise state. SubstitutingFigure 11 Equationscompares the (2) lift, and drag (3) coefficients, into Equation and (1), lift–to–drag the expression ratio at different of the relationship angles of attack between the fuelof the consumption clean wing, TPC, and theand lift-to-dragFADCW configurations. ratio is: A grid‐dependence study is conducted for the FADCW configuration and the results are also shown in this figure. The grid sizes used here are a 3 coarse grid of 3.7 million cells, a medium(FC) grid of 7.5C millionL 2 /CD cells, and a fine grid of 15 million cells. FADCW = TPC The results show that there is a good linear relationship 3 between. the lift coefficient (Figure 11a) (4) (FC)TPC C 2 /C and the angle of attack in the TPC and FADCW configurations,L D FADCW even if the propeller aerodynamic interference is strong and complex. The lift for the TPC and FADCW are almost the same for all Equationangles of attack. (4) indicates When that 4 the, the fuel lift coefficient consumption for the ratio FADCW between is slightly TPC and larger FADCW than that configurations of the is inverselyclean wing. proportional While the toopposite their ratio is true of CwhenL/CD, which4 . Therefore, means thatthe lift an slope aircraft for withFADCW a high decreases lift-to-drag ratioslightly (CL/CD by) has 3.8% a compared low fuel consumption with the clean atwing. the cruise state. FigureIn Figure11 compares 11b, the the drag lift, coefficient drag coe forffi cients,the FADCW and lift-to-dragbegins to be ratio smaller at dithanfferent that of angles the clean of attack  of thewing clean and wing, the TPC TPC, when and FADCW4 . The configurations. larger the angle of A attack, grid-dependence the greater the study decrement is conducted of the drag for the FADCWthat can configuration be obtained. and Benefiting the results from arethe alsodrag shownreduction, in thisthe lift–to–drag figure. The ratio grid for sizes the usedFADCW here is are a coarseaugmented grid of 3.7 apparently million cells, at large a medium range of grid. With of 7.5the million help of the cells, propeller and a fineinterference, grid of 15 the million FADCW cells. configuration has capabilities of decreasing the wing drag and increasing its aerodynamic efficiency.

(a) (b) (c)

Figure 11. Comparisons of aerodynamic forces for diﬀerent conﬁgurations (Ma = 0.1017, Ω = 4400 r/min): (a) C α,(b) C α,(c) C /C α. L − D − L D − Energies 2019, 12, 3911 11 of 16

The results show that there is a good linear relationship between the lift coefficient (Figure 11a) and the angle of attack in the TPC and FADCW configurations, even if the propeller aerodynamic interference is strong and complex. The lift for the TPC and FADCW are almost the same for all angles of attack. When α < 4◦, the lift coefficient for the FADCW is slightly larger than that of the clean wing. While the opposite is true when α > 4◦. Therefore, the lift slope for FADCW decreases slightly by 3.8% compared with the clean wing. In Figure 11b, the drag coefficient for the FADCW begins to be smaller than that of the clean wing and the TPC when α > 4 . The larger the angle of attack, the greater the decrement of the drag that − ◦ can be obtained. Benefiting from the drag reduction, the lift-to-drag ratio for the FADCW is augmented apparently at large range of α. With the help of the propeller interference, the FADCW configuration has capabilities of decreasing the wing drag and increasing its aerodynamic efficiency. For the further comparison, Table3 lists the detailed calculation results at an angle of attack of α = 2◦. It should be noted that all the changes in value in this table are relative to the clean wing.

Table 3. Comparisons of CL, CD, and CL/CD at α = 2◦ (Ma = 0.1017, Ω = 4400 r/min, medium grid).

Conﬁguration CL CD CL/CD Clean wing 0.4902 0.05092 9.63 TPC (∆Z/R = 0) 0.4957 0.05682 8.64 FADCW 0.4975 0.04562 10.91 Change (TPC) +1.12% +11.59% 10.28% − Change (FADC) +1.49% 10.41% +13.29% −

It is seen that the FADCW has a slight advantage over the TPC in increasing the wing lift. Considering the computational error; however, this advantage is so small that it can even be neglected. As for the drag coefficient, there is an increment of 11.59% for TPC but a decrement of 10.41% for the FADCW. As a result, the lift-to-drag ratios CL/CD of these two configurations are reduced and augmented by 10.28% and 13.29%, respectively. According to Equation (4), the fuel consumption ratio between FADCW and TPC configurations is

FC FADCW = 0.7985 FCTPC

This result means that the FADCW configuration can reduce the fuel consumption by 20.15% compared with the TPC configuration. So the comparisons described above demonstrate that it is effective for FADCW to make good use of the suction action in front of the propeller and the slipstream acceleration behind the propeller to improve the wing performance, especially for drag reduction. The design idea has been proven to be reasonable and successful. The primary advantage of the FADCW is its ability of reducing the drag. To be able to make sure of the reason for the decreased total drag in the FADCW, Table4 compares the pressure and skin-friction drag coefficients between the TPC and FADCW. For an intuitive observation, the results are given in terms of their respective increments compared to the clean wing. It is seen that with the favorable propeller influence, the pressure drag coefficient (denoted as CDP) of the wing in FADCW is reduced by 7.40%, and the skin friction drag coefficient C f is only 66.37% of that in TPC. Therefore, the decrease of the total drag in FADCW can be attributed to the simultaneous reduction in CDP and C f , which is contrary to the result of TPC. Figure 12 presents the pressure distribution for the TPC and FADCW, respectively. For the tractor propeller configuration shown in Figure 12a, the presence of the wing retards the high speed propeller slipstream and then causes the static pressure and the affected area at the leading edge of the wing (marked with a black oval dashed line) to be larger than those at other positions. Although the low pressure area on the upper surface of the wing covers about 90% of the wing span, the propeller Energies 2019, 12, x FOR PEER REVIEW 13 of 16

the low pressure area on the upper surface of the wing covers about 90% of the wing span, the propeller slipstream only increases the negative pressure of the wing in the slip zone and there is no apparent favorable interference in the region outside of the slip. For the FADCW shown in Figure 12b, the propeller and the main wing constitute an over–the–wing propeller arrangement. The influence of the propeller on the wing is mainly caused Energiesby2019 the, suction12, 3911 action in front of the propeller blade. Because of this effect, the negative pressure on12 of 16 the top surface of the main wing is enhanced further and the width of the influenced area along the wing span is enlarged to be at least four times the propeller radius, which are helpful in aiding a slipstreamconsiderable only increases reduction theof the negative pressures pressure drag coefficient of the wing for the in main the slip wing. zone In addition, and there the is aft no of apparent the favorablemain interferencewing’s top surface in the and region the bottom outside surface of the of slip. the induced wing form a rectangular duct. When the free stream approaches this duct gradually, its velocity will be increased because of the Tablecontraction 4. Comparison of the cross of dragarea of coe thisﬃcient duct, between which is the also TPC beneficial and FADCW. for the (Ma decrease= 0.1017, of Ωthe= main4400 wing’sr/min ,

αpressure= 2◦, medium drag. grid). Regarding the induced wing, the flow characteristics of the propeller–wing interaction shown in Figure 12a are also reflectedConﬁguration here. Since the chord∆CDP of the induced wing∆Cf is only 1/4 of that in TPC, the blocking effect caused byTPC the induced wing+ on10.30% the slipstream +is16.77% weakened significantly, which leads to a small pressure dragFADCW on the induced wing.7.40% 22.50% − −

(a) (b)

FigureFigure 12. Pressure12. Pressure distributions distributions in in TPC TPC andand FADCW configurations: conﬁgurations: (a) (TPC;a) TPC; (b) FADCW. (b) FADCW. (Ma = (Ma = 0.1017,  = 4400 r/min ,  =2 , medium grid). 0.1017, Ω = 4400 r/min, α = 2◦, medium grid).

For theThe FADCW main reason shown for the in Figure decreased 12b, skin the friction propeller drag and coefficient the main in wing the FADCW constitute configuration an over-the-wing is propellerthe considerable arrangement. reduction The influence of the wing of thearea propeller strongly washed on the wingby the is propeller. mainly caused In the byflow the field suction downstream of the propeller disk, most of the free stream turbulence is augmented due to the action in front of the propeller blade. Because of this effect, the negative pressure on the top surface of propeller interference, and it results in an increase of C for the portion of the wing submerged in the main wing is enhanced further and the width of the influencedf area along the wing span is enlarged the slipstream. Since the propeller is located over the main wing, there is no direct washing action of to be at least four times the propeller radius, which are helpful in aiding a considerable reduction of the slipstream on the main wing. Although indirect interaction between the propeller slipstream and the pressuresthe main dragwing coeexists,fficient it mainly for the occurs main at wing. the aft In of addition, the main the wing. aft ofTherefore, the main the wing’s area of top the surface main and the bottomwing affected surface by of the propeller induced wingis much form smaller a rectangular than that duct.in the When TPC. As the for free the stream induced approaches wing, a this ductsegment gradually, of itsit is velocity washed will strongly be increased and directly because by the of slipstream; the contraction however, of the the cross shortened area of chord this duct, whichreduces is also its beneficial wetted area for to the be decrease1/4 of the ofclean the wing main in wing’s Figure pressure4, and then drag. causes an apparent decrease

Regardingof C f . The calculated the induced result wing, indicates the flow that characteristicsthe skin friction ofdrag the of propeller-wing the induced wing interaction is about 20% shown of in Figurethe 12 originala are also wing. reflected here. Since the chord of the induced wing is only 1/4 of that in TPC, the blocking eFigureffect caused 13 describes by the the induced effect of wing the propeller on the slipstream rotation speed is weakened on the aerodynamic significantly, forces which of the leads to a smallwing pressure for the dragTPC and on theFADCW. induced The wing. results show that the lift and drag coefficients increase nearly Thelinear main with reasonthe augmentation for the decreased of the propeller skin friction rotation drag speed. coe Whenfficient  in4400 the FADCW r/min , the configuration FADCW is thebegins considerable to have a reductionlift–enhancing of thecapability. wing areaA maximal strongly increment washed of 11.07% by the relative propeller. to the In clean the flowwing field 7000 r/min downstreamcan be acquired of the propeller when the rotation disk, most speed of theis increased free stream to turbulence. The is augmented comparison duebetween to the the propeller lift curve slopes of the TPC and FADCW demonstrates that the FADCW has a higher growth rate for interference, and it results in an increase of C f for the portion of the wing submerged in the slipstream. C and its lift is more sensitive to the change of the propeller rotation speed. Regarding the drag Since theL propeller is located over the main wing, there is no direct washing action of the slipstream on the main wing. Although indirect interaction between the propeller slipstream and the main wing exists, it mainly occurs at the aft of the main wing. Therefore, the area of the main wing affected by the propeller is much smaller than that in the TPC. As for the induced wing, a segment of it is washed strongly and directly by the slipstream; however, the shortened chord reduces its wetted area to be 1/4 of the clean wing in Figure4, and then causes an apparent decrease of C f . The calculated result indicates that the skin friction drag of the induced wing is about 20% of the original wing. Figure 13 describes the effect of the propeller rotation speed on the aerodynamic forces of the wing for the TPC and FADCW. The results show that the lift and drag coefficients increase nearly linear with the augmentation of the propeller rotation speed. When Ω 4400 r/min, the FADCW begins ≥ to have a lift-enhancing capability. A maximal increment of 11.07% relative to the clean wing can be Energies 2019, 12, 3911 13 of 16 acquired when the rotation speed is increased to 7000 r/min. The comparison between the lift curve Energies 2019, 12, x FOR PEER REVIEW 14 of 16 Energies 2019, 12, x FOR PEER REVIEW 14 of 16 slopes of the TPC and FADCW demonstrates that the FADCW has a higher growth rate for CL and its liftcoefficient is more sensitiveshown in toFigure the change 13b, it is of seen the propellerthat the FADCW rotation reduces speed. the Regarding wing drag the for drag all of coe theffi cient coefficient shown in Figure 13b, it is seen that the FADCW reduces the wing drag for all of the showncalculation in Figure speeds. 13b, it Although is seen that the the CD FADCW has a maximum reduces at the  wing=7000r/min drag for, it all still of decreases the calculation by 2.16% speeds. calculation speeds. Although the CD has a maximum at  =7000r/min, it still decreases by 2.16% Althoughcompared the Cwithhas the a maximumclean wing. atDueΩ to= 7000the decreasedr/min, it drag, still decreasesthe lift–to–drag by 2.16% ratio comparedof the FADCW with the compared withD the clean wing. Due to the decreased drag, the lift–to–drag ratio of the FADCW increases for all of the rotation speeds and the maximum occurs at  = 5000 r/min , where the cleanincreases wing. Due for toall theof the decreased rotation drag,speeds the and lift-to-drag the maximum ratio occurs of the at FADCW  = 5000 increases r/min , where for all the of the increment reaches 14.45%. = rotationincrement speeds reaches and the 14.45%. maximum occurs at Ω 5000 r/min, where the increment reaches 14.45%.

(a) (b) (c) (a) (b) (c) Figure 13. The effect of the propeller rotation speed on TPC and FADCW (Ma = 0.1017,  =2 , Figure 13. The effect of the propeller rotation speed on TPC and FADCW (Ma = 0.1017,  =2 , Figuremedium 13. The grid): effect (a) of C the  propeller  ; (b) rotationC   speed ; (c) on CC TPC and  FADCW (Ma = 0.1017, α = 2◦, medium medium grid): (a) CL   ; (b) CD   ; (c) CCL D   . grid): (a) C Ω;(b) C L Ω;(c) C /C D Ω. L D . L − D − L D − Figure 14 compares the pressure distribution of y/b = 0 at different propeller rotation speeds. FigureFigure 14 compares 14 compares the the pressure pressure distribution distribution of of y/b y/b == 0 0at at different different propeller propeller rotation rotation speeds. speeds. When  = 2000 r/min , the pulling force of the propeller is almost zero and the suction action in front WhenWhenΩ = 2000 = 2000r/min r/min, the, the pulling pulling force force of of thethe propeller is is almost almost zero zero and and the the suction suction action action in front in front of the propeller blade is so slight that it fails to produce a significant acceleration on the air flowing of theof propeller the propeller blade blade is so is so slight slight that that it it fails fails to to produceproduce a a significant significant acceleration acceleration on the on theair flowing air flowing across the upper surface of the main wing. Once the rotation speed increases (see Figure 14b); across the upper surface of the main wing. Once the rotation speed increases (see Figure 14b); acrosshowever, the upper the surface enhanced of suction the main effect wing. strengthens Once the the rotation negative speed pressure increases on the (see wing’s Figure upper 14 b);surface however, however, the enhanced suction effect strengthens the negative pressure on the wing’s upper surface the enhancedand in front suction of the eff propellerect strengthens disk, as the a result, negative the pressure chordwise on range the wing’s of this upper low pressure surface zone and inis front and in front of the propeller disk, as a result, the chordwise range of this low pressure zone is of theenlarged. propeller In disk, addition, as a result,for a high the chordwiserotation speed, range the of stronger this low slipstream pressure zonebehind is the enlarged. propeller In also addition, enlarged. In addition, for a high rotation speed, the stronger slipstream behind the propeller also for aincrease high rotation greatly speed, the suction the stronger force on slipstream the top surface behind of the the propeller induced also wing, increase which greatlyimproves the the suction increase greatly the suction force on the top surface of the induced wing, which improves the contribution of the induced wing lift to the total one from 10.4% (  = 2000 r/min ) to 12.5% forcecontribution on the top surface of the ofinduced the induced wing wing,lift to whichthe total improves one from the 10.4% contribution (  = 2000 of the r/min induced) to 12.5% wing lift to the(  total= 4000 one r/min from). 10.4%Regarding (Ω = the2000 compositionr/min) toof 12.5%the drag, (Ω the= induced4000 r/ minwing). maintains Regarding a contribution the composition (  = 4000 r/min ). Regarding the composition of the drag, the induced wing maintains a contribution of theof drag, about the 19% induced for all calculated wing maintains rotation aspeeds. contribution of about 19% for all calculated rotation speeds. of about 19% for all calculated rotation speeds.

(a) (b) (a) (b) Figure 14. Pressure contours at different rotation speeds: (a) 2000 r/min; (b) 4000 r/min. (Ma = 0.1017, FigureFigure 14. Pressure 14. Pressure contours contours at at di differentfferent rotation rotation speeds:speeds: ( (aa)) 2000 2000 r/min; r/min; (b ()b 4000) 4000 r/min. r/min. (Ma ( =Ma 0.1017,= 0.1017,  =2 , medium grid). α = 2◦,=2 medium , medium grid). grid). 4. Conclusions 4. Conclusions4. Conclusions This paper proposes a fuel saving double‐channel wing (FADCW) configuration and ThisThis paper paper proposes proposes a fuel a saving fuel double-channelsaving double‐channel wing (FADCW) wing (FADCW) configuration configuration and investigates and investigates its aerodynamic performance using the CFD method. The basic idea of the FADCW its aerodynamicinvestigates performanceits aerodynamic using performance the CFD method.using the The CFD basic method. idea The of the basic FADCW idea of configuration the FADCW is to

Energies 2019, 12, 3911 14 of 16 improve the lift-to-drag ratio and thus reduce the fuel consumption by making use of the favorable effects of a propeller. For the tractor propeller-wing arrangement analyzed in this paper, the propeller slipstream washes the wing directly and strongly and increases the wing lift and drag. The results indicate that there is a small augmentation in lift while the wing drag is increased by 11.59%, which leads to a detrimental reduction of 10.28% in the lift-to-drag ratio of the wing compared with an isolated wing with the same reference area. Except for the slipstream behind the propeller disk, a suction action is also generated in front of the propeller disk. Although this effect induces a relatively smaller velocity increment compared with the slipstream, its influencing scope on the free stream is at least twice that of the slipstream. The FADCW configuration combines advantages of a tractor propeller configuration and an over-the-wing propeller configuration. Hence, it can make use of the suction effect upstream of the propeller and the slipstream acceleration downstream of the propeller to improve the aerodynamic performance of the wing. With the aid of the propeller, the FADCW increases the lift-to-drag ratio by 13.29% and reduces the fuel consumption by 20.15% compared with the TPC. It proves that the design idea presented in this paper is shown to be feasible to reduce the fuel consumption of a propeller-driven aircraft and thus enlarges its range or loiter time.

Author Contributions: Conceptualization, H.W. and W.G.; methodology, H.W. and W.G.; software, H.W.; validation, W.G. and D.L; formal analysis, H.W. and W.G.; writing—original draft preparation, H.W.; writing—review and editing, W.G. and D.L. Funding: This research was funded by the National Natural Science Foundation of China (Grant No. 11902018) and the Pre-Research Field Fund of Equipment of China (Grant No. 61402060103 and No.61403110103). Conﬂicts of Interest: The authors declare no conﬂicts of interest.

Nomenclature

Re Reynolds number, Re = ρVl/µ C wing chord, m 3 ρ density of air, kg/m Cmain chord of the main wing for FADCW, m axial position of propeller centerline l reference length, m ∆X/R relative to the wing leading edge vertical position of propeller centerline µ dynamic viscosity ∆Z/R relative to the wing leading edge Mach number, Ma = free-stream Ma C thrust coefficient, C = T/ρπΩ2R4 velocity/sound speed T T α angle of attack CL lift coefficient R propeller or rotor radius, m CD drag coefficient r/R radial coordinate along rotor radius CL/CD lift-to-drag ratio Ω propeller or rotor rotation speed, r/min C f skin friction drag coefficient pressure coefficient, CP 2 CDP pressure drag coefficient Cp = (P P )/ 1/2ρV − ∞ ∞ P static pressure, pa ∆C f increment of skin friction drag coefficient X/C streamwise coordinate along wing chord ∆CDP increment of pressure drag coefficient b semi span of wing, m ∆VX increment of axial free stream velocity y/b spanwise position along wing span V free stream velocity ∞

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