Aerodynamic Performance of an Octorotor SUAV with Different Rotor Spacing in Hover

processes

Article Aerodynamic Performance of an Octorotor SUAV with Diﬀerent Rotor Spacing in Hover

Yao Lei 1,2,* , Yuhui Huang 1 and Hengda Wang 1

1 School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou 350116, China; [email protected] (Y.H.); [email protected] (H.W.) 2 Key Laboratory of Fluid Power and Intelligent Electro-Hydraulic Control (Fuzhou University), Fujian Province University, Fuzhou 350116, China * Correspondence: [email protected]

Received: 3 October 2020; Accepted: 26 October 2020; Published: 28 October 2020

Abstract: To study the aerodynamic performance of hovering octorotor small unmanned aerial vehicles (SUAV) with different rotor spacing, the computational fluid dynamics (CFD) method is applied to analyze the flow field of an octorotor SUAV in detail. In addition, an experimental platform is built to measure the thrust and power of the rotors with rotor spacing ratios L/D of 1.0, 1.2, 1.4, 1.6, and 1.8, sequentially. According to the theory of momentum, rotor aerodynamic performance is obtained with qualitative analysis. Further analysis with numerical simulation is presented with the flow field of the octorotor SUAV, the vorticity distribution, velocity distribution, pressure distribution, and streamline. The results show that the aerodynamic performance varies with the rotor spacing. Specifically, the aerodynamic performance is poor at L/D = 1.0, which is accompanied with strong interaction of wake and tip vortexes and interaction with each other. However, the aerodynamic efficiency is much improved with a larger rotor spacing, especially achieving the highest at L/D = 1.8, which is considered to be the best rotor spacing ratio for this kind of octorotor SUAV.

Keywords: octorotor SUAV; aerodynamic performance; rotor spacing; hover; CFD; vortices distribution

1. Introduction Small unmanned aerial vehicles (SUAVs) are normally less than 25 kg and easy to pack. Especially, the octorotor SUAVs with evenly distributed rotors have been widely used in agricultural, surveillance, and military, due to its advantages of simple operation and convenient portability. In addition, octorotor SUAVs have higher load and more damaged redundancy as compared with a quadrotor or hex-rotor SUAVs. Considering that octorotor SUAVs often operate in environments where the Reynolds numbers are less than 105, viscosity, laminar separation bubbles, thickened boundary layer, and flow separation influence the rotor tip, which can lead to increased drag on the vehicle, thus, resulting in poor aerodynamic performance. Especially, there is a strong vibration at higher rotor speed which can affect the dynamic stability of a rotorcraft [1–3]. There are two main ways to improve the aerodynamic performance of small rotary-wing UAVs. One way is to change the parameters of the blade [4], such as changing the shape of the blade platform, adding a twist, taper, and so on. The second way is to change the layout and configuration of the rotors, such as changing the distance between adjacent rotors, the number of rotors, the tilt angle of the rotors, and so on. At the same time, with the help of constantly developing computer simulation technology, we can intuitively explore the reasons that lead to a decrease or increase in aerodynamic performance of the rotor, and help to optimize the layout of the SUAVs.

Processes 2020, 8, 1364; doi:10.3390/pr8111364 www.mdpi.com/journal/processes Processes 2020, 8, 1364 2 of 12

Early studies have focused on hover performance analysis of a small single rotor and a small coaxial rotor. Bohorquez [5–7] experimentally measured the aerodynamic performance of the rotor and used fluorescent oil to visualize surface flow, which showed consistently poor performance for a variety of rotors with low Reynolds numbers (less than Re = 0.5 105). Ramasamy [8] used the tip × digital particle image velocimetry (DPIV) to study the aerodynamic efficiency of the hovering micro rotor with different blade shapes and found that changing the shape of the blade, such as adding a linear twist and changing the planform of the airfoil, could effectively improve the aerodynamic performance of the blade. A series of parametric studies of hovering coaxial rotor were conducted by Lakshminarayanan [9] and Syal [10]. Changing the inter-rotor spacing proved to influence the aerodynamic of the coaxial rotor in hover. In recent years, research on aerodynamic performance of small rotorcrafts has deepened. Yoons [11] studied the influence of the turbulence model on the flow solution accuracy of hovering rotor. High-fidelity computational fluid dynamics (CFD) simulations have been implemented for multi rotor [12,13], and adding components under the airframe was found to weaken the interactions between rotors. Henricks [14,15] investigated the effect of rotor variables on the aeroacoustics performance of a hovering rotor. Greater twist and taper were proven to improve both the aerodynamic and acoustic performance. A high-speed stereo particle-image velocimetry (SPIV) study on multi rotor was conducted by Shukla [16,17], and vortex–vortex, blade–vortex, and vortex–duct interactions were visualized. The effect of a tilting rotor on the aerodynamic performance was studied by Zhang [18]. Tilting has been shown to help keep the vehicle stable. The simulation of the downwash flow of octorotor was done by Yang [19]. The current study of rotor aerodynamic performance concentrated on the coaxial rotor and quadrotor since the rotor interference of an octorotor SUAV is relatively complicated, especially the different vortex–vortex and blade–vortex interactions with different rotor spacing. Therefore, analysis of the aerodynamic performance of octorotor is challenging work, which can also provide significant guidance for designing octorotor SUAVs. The main research objective of this paper is to explore how the aerodynamic performance of a small octorotor SUAV changes with a change of rotor spacing, why it changes, and whether there is an optimal rotor spacing. In comparison with previous studies on small quadrotor and small hex-rotor SUAVs [20–22], the improvement of this study lies in the addition of preliminary studies on wake vortices.

2. Theoretical Analysis Momentum theory is assumed to be an effective method for flow-field analysis of rotorcrafts. It regards the rotating rotor as an actuator disk and relates the induced airflow velocity through the actuator disk to the thrust and power of the rotor. According to the momentum theory [23], the induced flow velocity can be expressed as: p Vh = T/2ρA (1) where T is the thrust generated by the rotor, ρ is the air density, with a value of 1.225 kg m 3, and A is · − the area of the rotor disk. The induced power consumption can be expressed as:

3/2 p Pi = TVh = T / 2ρA (2)

To measure the aerodynamic eﬃciency of a rotor in hover, FM is deﬁned as the ratio of induced power consumption to actual power consumption:

p 3/2 P T3/2/ 2ρA C / √2 FM = i = = T (3) P P CP Processes 2020, 8, 1364 3 of 12 where T Processes 2020, 8, x FOR PEER REVIEW CT = 3 of(4) 12 ρAΩ2R2 is the thrust coefficient, T = CT P 22 (4) CP = ρΩA R (5) ρAΩ3R3 is the thrust coefficient, is the power coefficient. Ω is the angular velocity of the rotor and R is the radius of the rotor. P FM of a given rotor is often expressed as a= function of CT/σ. Here, σ is the solidity of the rotor, CP 33 (5) and can be defined as: ρΩA R is the power coefficient. Ω is the angular velocityσ = Nc /ofπ theR rotor and R is the radius of the rotor. (6) σ σ whereFMN ofis thea given number rotor of is blades often and expressedc is the as chord. a function of CT / . Here, is the solidity of the rotor,Since and can the be tapered defined blade as: is adopted in this paper, the influence of varying chord length on the solidity must be considered, and Equation (7)σπ is= adopted to calculate the equivalent solidity: Nc/ R (6) Z 1 where N is the number of blades and c is the chord. 2 σe = 3 σr dr (7) Since the tapered blade is adopted in this paper,0 the influence of varying chord length on the solidity must be considered, and Equation (7) is adopted to calculate the equivalent solidity: The total efficiency of the aircraft is determined by the power loading: 1 σσ= 2 e 3 rdr (7) T 0 C PL = = T (8) The total efficiency of the aircraft is determinedP CbyPΩ theR power loading:

T CT Combined with momentum theory, PLPLcan= also= be expressed in the following form: (8) P CRΩ p P 2ρFM Combined with momentum theory, PLPL can= also be expressed in the following form: (9) √DL 2ρ FM PL= (9) where DL is the disk loading and can be deﬁned as: DL where DL is the disk loading and can be definedDL =as:T /A (10) DL=/ T A (10) In addition, the tip chord Reynolds number in this paper is deﬁned by the chord length at 0.75R: In addition, the tip chord Reynolds number in this paper is defined by the chord length at 0.75R:

Retip ==ρρμVc0.75/µ (11) Retip Vc0.75 / (11)

− where µμisis kinematic kinematic viscosity viscosity coe coefficiﬃcientent of of air, air, with with a value a value of 1.79of 1.7910×⋅ 105 Pa5 Pass withwith a temperaturea temperature of × − · of293.15 293.15 K, K, and and a pressure a pressure of 101.325of 101.325 kPa. kPa. Figure 11 shows shows thethe arrangementarrangement ofof octorotoroctorotor andand interferenceinterference between between adjacent adjacent rotors. rotors.

Inflow Rotor spacing R

Ω Interference Outflow Outflow

Figure 1. SketchSketch of the octorotor arrangement.

3. Hover Experiment

3.1. Experimental Setup

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3. Hover Experiment

3.1.Processes Experimental 2020, 8, x FOR Setup PEER REVIEW 4 of 12 The rotor used in this paper is made of carbon fiber, and unidirectional carbon fiber cloth is used The rotor used in this paper is made of carbon fiber, and unidirectional carbon fiber cloth5 is used as reinforcement. The weight of one rotor is 15 g. The rotor is operating at Retip = 0.59 10 ~0.99 × 5 × 5 10as5. reinforcement. The specific rotor The parameters weight of one are shownrotor is in 15 Table g. The1. rotor is operating at Retip = 0.59 × 10 ~0.99 × 10 . The specific rotor parameters are shown in Table 1. Table 1. Rotor parameters. Table 1. Rotor parameters. Chord (mm) Radius (m) Solidity Pitch (m) Twist Chord (mm) Radius (m) Solidity Pitch (m) Twist 28 0.2 0.09 0.157 0 28 0.2 0.09 0.157 0

TheThe schematic schematic diagram diagram of of the the test test bench bench is is shown shown in in Figure Figure2. 2. Each Each rotor rotor is is fitted fitted with with a separatea separate motormotor and and thrust thrust sensors sensors (model (model CZL601, CZL601, accuracy accuracy 0.02%±0.02% F.S., F.S., range range 0~3 0~3 kg). kg). Adjacent Adjacent rotors rotors rotate rotate ± inin opposite opposite directions, directions, and and the the rotor rotor speed speed is is measured measured with with an an optical optical tachometer tachometer (model (model DT2234C, DT2234C, accuracyaccuracy 0.05±0.05 n% n%+ +1 1 d). d). To To reduce reduce the the impact impact brought brought by by the the ground ground eff ect,effect, the the rotor rotor is installed is installed at a at ± heighta height of 1.5 of m1.5 above m above the ground. the ground. Rotor Rotor spacing spacingL is defined L is defined as the distance as the distance between between the rotor the centers rotor ofcenters two adjacent of two rotors.adjacent In rotors. this experiment, In this experiment,L = 400, L 480, = 400, 560, 480, 640, 560, and 640, 720 and mm, 720 respectively. mm, respectively. Thus, theThus, corresponding the corresponding dimensionless dimensionless spacing ratiosspacingL/ Dratios= 1.0, L/ 1.2,D = 1.4,1.0, 1.6,1.2, and1.4, 1.6, 1.8 (andD is 1.8 the (D diameter is the diameter of the rotor).of the By rotor). changing By changing the tip chord the tip Reynolds chord number,Reynolds the number, thrust andthe powerthrust consumptionand power consumption generated bygenerated the octorotor by the at fiveoctorotor spacing at arefive collected,spacing are and collected, the aerodynamic and the aerodynamic performance ofperformance the octorotor of isthe analyzedoctorotor accordingly. is analyzed accordingly.

Propeller Motor

Remote control

Thrust sensor PCB

Thrust Tachometer Power Data acquisition Rotor speed Current Voltage system

Figure 2. Schematic diagram of test bench. Figure 2. Schematic diagram of test bench. 3.2. Error Analysis 3.2. Error Analysis The main sources of error in the experiments are the standard deviations of the rotational speed and theThe mean main voltages sources from of error the forcein the sensors. experiments Typical are values the standard of the standard deviations deviations of the rotational of thrust speed are aboutand the 1% mean of the voltages mean values. from the Rotational force sensors. speed Typical error is values related of to the the standard ﬁnite number deviations of magnets of thrust that are exciteabout the 1% tachometer, of the mean which values. causes Rotational an error speed of 1 /error24 is60 related= 2.5 RPM. to the The finite statistical number (random) of magnets error that × inexcite the coe theﬃ tachometer,cient values which for each causes run wasan error estimated of 1/24 by × 60 the = standard2.5 RPM. deviationThe statistical of repeated (random) samples. error in Thisthe experimentcoefficient values mainly for measured each run variable was estimated as thrust byT, the torque standardQ, and deviation rotational of speed repeatedΩ. To samples. determine This theexperiment accuracy of mainly the test measur measurements,ed variable a normalizedas thrust T, criterion torque Q is, neededand rotational in this casespeed [24 –Ω26.]. To Consider determine a the accuracy of the test measurements, a normalized criterion is needed in this case [24–26]. Consider

a variable X i , the uncertainty of the calculated results can be expressed by using the ”Kline– McClintock”’ equation [27]:

2 1/2 N ∂R ΔΔ= RXi (12) = ∂X i 1 i Δ where X i is the uncertainty of X i .

Processes 2020, 8, 1364 5 of 12

variable Xi, the uncertainty of the calculated results can be expressed by using the ”Kline–McClintock”’ equation [27]:  1/2  N !2 X ∂R  ∆R =  ∆Xi  (12)  ∂Xi  i=1  Processes 2020, 8, x FOR PEER REVIEW 5 of 12 where ∆Xi is the uncertainty of Xi. The expression of uncertainty of power can be obtained as follows: The expression of uncertainty of power can be obtained as follows: s !22 !2 2 ∂∂∂PPP ∂P ∆ΔΔPPQ==+∆Q +∆Ω ΔΩ (13)(13) ∂∂∂QQ ∂ΩΩ

TheThe uncertainty uncertainty of of PP asas a a percentage percentage is: is: ΔΔs 2 ΔΩ2 PQ !2  ∆P =+∆Q  ∆Ω 2 (14) PQ= +Ω (14) P Q Ω Similarly: Similarly: s 222 ΔΔPL T2  Δ Q!2  ΔΩ2  ∆PL =+−+−∆T ∆Q ∆Ω (15) = ++ Ω  (15) PL  TT − Q − Ω  s 22 !2 2 ΔΔΔΔΩ∆FMFM 33 ∆ TT 2 ∆Q Q ∆Ω 2  =+−+−= + + (16)(16) FM 2 T − Q − Ω  FM2 T Q Ω  By calculation, the uncertainty of P, PL, and FM is 1.41%, 1.44%, and 1.51%, respectively. The values By calculation, the uncertainty of P, PL, and FM is 1.41%, 1.44%, and 1.51%, respectively. The of uncertainty that are presented in this study are all calculated for 95% conﬁdence levels. values of uncertainty that are presented in this study are all calculated for 95% confidence levels. 3.3. Results 3.3. Results The thrust and power consumption of the octorotor with diﬀerent spacing ratios is shown in FigureThe3. thrust and power consumption of the octorotor with different spacing ratios is shown in Figure 3.

(N) L/D=1.8

T 22 L/D=1.6 20 L/D=1.4 L/D=1.2 18 L/D=1.0 16 8 single rotor

12 100 150 200 250 300 350 400 P (W)

FigureFigure 3. 3. ThrustThrust and and power power consumption consumption variation. variation.

ItIt can can bebe seenseen from from Figure Figure3 that 3 that at theat samethe same power power consumption, consumption, the thrust the thrust is significantly is significantly greater greaterthan the than simple the superpositionsimple superposition of the thrust of the generated thrust generated by the eight by the small eight single small rotors. single In rotors. addition, In addition,the thrust the generated thrust generated by the octorotor by the octorotor at L/D = at1.0 L/D is = significantly 1.0 is significantly lower thanlower that than generated that generated by the byoctorotor the octorotor at the at other the fourother spacing four spacing ratios. ratios. It indicates It indicates that thethat rotor the rotor interference interference with with proper proper rotor rotorspacing spacing is beneficial is beneficial to improve to improve the hover the hover efficiency efficiency of the of octorotor. the octorotor. TheThe variation variation of of FMFM withwith different different rotor rotor spacing spacing ratios is shown in Figure 44..

Processes 2020, 8, 1364 6 of 12 Processes 2020, 8, x FOR PEER REVIEW 6 of 12

Processes 2020, 8, x FOR PEER REVIEW0.360 6 of 12 0.355 0.3500.360 0.3450.355 0.3400.350 0.3350.345 0.3300.340 0.3250.335 0.3200.330 0.325 FM 0.315 L/D=1.8 0.320 0.310 L/D=1.6

FM 0.315 0.305 L /LD/=1.8D=1.4 0.310 L /LD/=1.6D=1.2 0.300 0.305 L /LD/=1.4D=1.0 0.295 L/D=1.2 0.300 0.290 L/D=1.0 0.295 0.285 0.290 0.2800.285 55000 60000 65000 70000 75000 80000 85000 90000 0.280 55000 60000 65000 70000Re 75000 80000 85000 90000 Re FigureFigure 4. 4. VariationVariation of of the the figure figure of of merit. Figure 4. Variation of the figure of merit. ItIt can can be be found found from from Figure Figure 44 thatthat thethe FMFM ofof the the octorotor octorotor shares shares a a similar similar tendency, tendency, and and it it is is It can be found from Figure 4 that the FM of the octorotor shares a similar tendency, and it is veryvery interesting interesting to to note note that that there there is is a asudden sudden drop drop at at ReRe = =7924679246 for for L/DL/ D= 1.2= 1.2and and at Re at =Re 71,321= 71,321 for very interesting to note that there is a sudden drop at Re = 79246 for L/D = 1.2 and at Re = 71,321 for Lfor/D L=/ D1.0.= 1.0.The Thelikeliest likeliest explanation explanation for this for thisphenomenon phenomenon is the is collapse the collapse of the of suction the suction forces forces on the on L/D = 1.0. The likeliest explanation for this phenomenon is the collapse of the suction forces on the tipthe and tip andthe theincrease increase in vibration in vibration caused caused by by the the flow flow separation, separation, which which are are relatively relatively unsteady unsteady for for tip and the increase in vibration caused by the flow separation, which are relatively unsteady for smallersmaller rotor rotor spacing, spacing, where where the the rotor rotor is is apt apt to to ha haveve somewhat somewhat greater greater interaction interaction with with its its own own wake. wake. smaller rotor spacing, where the rotor is apt to have somewhat greater interaction with its own wake. ThisThis heightened heightened interaction interaction is is reflected reflected in in the the greater greater variability variability to to a a decrease decrease in in FMFM.. Furthermore, Furthermore, This heightened interaction is reflected in the greater variability to a decrease in FM. Furthermore, because of the unpredictable inflow and outflow of smaller rotor spacing where the rotor is apt to have becausebecause of ofthe the unpredictable unpredictable inflow inflow and and outflowoutflow of smaller rotorrotor spacing spacing where where the the rotor rotor is isapt apt to to interaction with its own wake, it is, therefore, not entirely surprising that some data do not follow havehave interaction interaction with with its its own own wake, wake, itit is,is, therefore,therefore, not entirelyentirely susurprisingrprising that that some some data data do do not not the same trends. Additionally, the aerodynamic performance at L/D = 1.8 is much better than other followfollow the the same same trends. trends. Additionally, Additionally, the the aerodynamicaerodynamic performanceperformance at at L L/D/D = =1.8 1.8 is is much much better better than than otherspacingother spacing spacing ratios ratios with ratios awith muchwith a amuch highermuch higher higherFM. FM FM.. TheTheThe variation variation variation of of of power power loading loading versus versus disk disk loading isis shownshown in in Figure Figure 5.5 5. .

0.140.14 L L/D/D=1.8=1.8 L L/D/D=1.6=1.6 0.13 0.13 L L/D/D=1.4=1.4 L L/D/D=1.2=1.2 L/D=1.0 0.120.12 L/D=1.0

0.11 0.11 (N/W) (N/W) PL

PL 0.10 0.10

0.09 0.09

0.08 0.08 12 14 16 18 20 22 24 26 28 30 32 34 12 14 16 18 20 22 24 26 28 30 32 34 DL (N/m2) 2 DL (N/m ) FigureFigure 5.5. VariationVariation of power loading loading and and disk disk loading. loading. Figure 5. Variation of power loading and disk loading. AsAs can can be be seen seen from from Figure Figure5 ,5,PL PL valuevalue at L//D == 1.81.8 always always is ishigher higher than than the the other other rotor rotor spacings. spacings. TheThePLAs PL forcan for 1.4 be 1.4 andseen and 1.2 from 1.2 are are Figure approximately approximately 5, PL value thethe at samesame L/D = with 1.8 always a a lower lower is value. value. higher Especially, Especially, than the theother the PLPL rotor forfor L /spacings.DL/ D= 1.0= 1.0 Thewaswas PL presented presented for 1.4 and with with 1.2 lowest lowestare approximately value value which which susuthefffferedered same fromfrom with strong a lower rotor value. interference. interference. Especially, the PL for L/D = 1.0 was presentedToTo sum sum up, up,with when when lowest the the spacing value spacing which ratio ratio is su is 1.8,ffered 1.8, the the smallfrom small octorotorstrong octorotor rotor has has interference. better better aerodynamic aerodynamic e ffiefficiencyciency and totalandTo effi total sumciency, efficiency, up, and when therefore and the therefore spacing it can be itratio regardedcan isbe 1.8, regarded as the the small best as the rotoroctorotor best spacing rotor has spacing in better the current inaerodynamic the current working working efficiency condition. andcondition. totalThe FMefficiency, comparison and therefore of the small it can octorotor, be regarded the small as the quadrotor best rotor [ 21spacing], and thein the small current hex-rotor working [20] condition.at the optimumThe FM comparison rotor spacing of the is shownsmall octorotor, in Figure the6. small quadrotor [21], and the small hex-rotor [20] at Thethe optimum FM comparison rotor spacing of the issmall shown octorotor, in Figure the 6. small quadrotor [21], and the small hex-rotor [20] at the optimum rotor spacing is shown in Figure 6.

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0.3600.360 octo-rotor octo-rotor 0.3550.355 quadrotor quadrotor [21] [21] hex-rotor hex-rotor [20] [20] 0.3500.350

0.3450.345

0.3400.340 FM FM 0.3350.335

0.3300.330

0.3250.325

0.320 0.320

55000 60000 65000 70000 75000 80000 85000 90000 55000 60000 65000 70000 75000 80000 85000 90000 Re Re Figure 6. The FM comparison with quadrotor and hex-rotor. FigureFigure 6.6. The FM comparison with quadrotor and and hex-rotor. hex-rotor.

It can be seen from Figure 6 that the aerodynamic performance of a small octorotor is much ItIt can can be be seen seen from from Figure Figure6 that 6 that the aerodynamicthe aerodynamic performance performance of a smallof a small octorotor octorotor is much is much better better than that of a small quadrotor and a small hex-rotor composed of the same rotor. thanbetter that than of athat small of a quadrotor small quadrotor and a small and a hex-rotor small hex-rotor composed composed of the sameof the rotor.same rotor. 4. Numerical4. Numerical Simulation Simulation 4. Numerical Simulation 4.1.4.1. Simulation Simulation Setting Setting and and Mesh Mesh Analysis Analysis 4.1. Simulation Setting and Mesh Analysis ToTo further further analyze analyze the the aerodynamic aerodynamic performance performance of of the the small small octorotor, octorotor, the the flow flow field field of theof the small To further analyze the aerodynamic performance of the small octorotor, the flow field of the5 octorotorsmall octorotor with diff erentwith different spacing ratiosspacing was ratios numerically was numerically simulated simulated with ANSYS with when ANSYS Re tipwhen= 0.79 Retip =10 . small octorotor with different spacing ratios was numerically simulated with ANSYS when Re×tip = The0.79 detailed × 105. The mesh detailed distribution mesh distribution is shown in is Figure shown7 .in Figure 7. 0.79 × 105. The detailed mesh distribution is shown in Figure 7.

Rotationary region Rotationary region

Stationary region Stationary region Interface Rotor refinement Interface Rotor refinement Rotor tip Rotor tip Figure 7. Mesh distribution. FigureFigure 7.7. Mesh distribution. The whole computational domain is divided into nine regions including one cylinder stationary regionTheThe and whole whole eight computational computational cylinder rotating domaindomain regions isis divided divided(to capture into the nine flow regions detail ofincluding including four rotors one one with cylinder cylinder refined stationary stationary mesh), regionregionwhich and and has eight eight a total cylinder cylinder size of rotatingrotating70 million regionsregions cells. In (to(to additi captureon, thethe flow flowSUAV detail detail is located of of four four in rotors rotorsthe upper with with refinedregion refined of mesh), mesh),the domain to obtain the detail of the downwash flow of the SUAV. To handle the low Reynolds number whichwhich has has a a total total size size ofof 7070 millionmillion cells.cells. In addition,addition, the SUAV is located in in the the upper upper region region of of the the flows, multiple viscous boundary layers are used in the simulations, and the max element metrics is domaindomain to to obtain obtain thethe detaildetail ofof thethe downwash flow flow of of the the SUAV. SUAV. To handle the the low low Reynolds Reynolds number number below 0.8 to capture the flow detail of the rotor tip and the interfaces between stationary and rotating flows,flows, multiple multiple viscous viscous boundaryboundary layerslayers areare usedused in the simulations, and and the the max max element element metrics metrics is is regions. The grid is considered to be sufficient to handle these simulations and the mesh on the rotor belowbelow 0.8 0.8 to to capture capture thethe flowflow detaildetail ofof thethe rotor tip and the interfaces interfaces between between stationary stationary and and rotating rotating regions.tip is refined The grid to reachis considered the independence to be sufficient state. toFor handle the boundary these simulations conditions, and all threethe mesh surfaces on the of rotorthe regions.cylinder The domain grid is are considered set as no to slip be suwallfficient where to handlethe rotating these region simulations and stationary and the mesh overlap on the is rotorset as tip tip is refined to reach the independence state. For the boundary conditions, all three surfaces of the is refinedinterface. to reachThe sliding the independence mesh is used state. for the For transient the boundary solver. conditions, The Spalart–Allmaras all three surfaces turbulence of the model cylinder cylinder domain are set as no slip wall where the rotating region and stationary overlap is set as domainwas chosen are set for as the no RANS slip wall closure where which the rotatingwas proven region to be and capable stationary of ha overlapndling the is setaerodynamic as interface. interface. The sliding mesh is used for the transient solver. The Spalart–Allmaras turbulence model Theperformance sliding mesh of isthe used multi-rotors, for the transient especially solver. at low The Re Spalart–Allmaras. The physical time turbulence step corresponds model to was a rotor chosen forwas the chosen RANS for closure the RANS which wasclosure proven which to bewas capable proven of handlingto be capable the aerodynamic of handling performancethe aerodynamic of the performance of the multi-rotors, especially at low Re. The physical time step corresponds to a rotor

Processes 2020, 8, x FOR PEER REVIEW 8 of 12

Processes 2020, 8, 1364 8 of 12 rotation of 30 degrees, and 12 steps correspond to a rotor revolution. The rotor made a total of 40 revolutions. Furthermore, the mesh independence study is conducted to show that the results are Processes 2020, 8, x FOR PEER REVIEW 8 of 12 multi-rotors,already reaching especially the grid at lowindependenceRe. The physical state. time step corresponds to a rotor rotation of 30 degrees, androtation 12For steps the of correspond numerical30 degrees, simulation, toand a rotor12 steps revolution. the correspond accuracy The toof rotor athe rotor mademodel revolution. a totalused, of theThe 40 quality revolutions.rotor made of the a Furthermore, totalmesh, of the40 theselectedrevolutions. mesh boundary independence Furthermore, conditions, study the the ismesh conductedturbulence independence model, to show studyand that the is the discreteconducted results format areto show already all produce that reaching the some results theerrors. are grid independenceForalready the experiment, reaching state. the thegrid sensorindependence error is state. the main error source. The comparison between the experimentalForFor the the numerical and numerical simu simulation,lation simulation, results the ofthe accuracy FM accuracy of octorotor of the of modelthe is shownmodel used, used,in the Figure quality the 8.quality of the of mesh, the mesh, the selected the boundaryselectedIt can conditions,boundary be seen that conditions, the the turbulence simulation the turbulence model, results and model,are theslightly discreteand the higher discrete format than allformat the produce experiment, all produce some with errors.some an errors.For error the experiment,of Forabout the 6%, experiment, the which sensor may errorthe be thesensor is theresult mainerror of the erroris introducedthe source. main The errorCP comparisonin experimentssource. The between andcomparison the the extra experimental between validation the andof simulationCPexperimental for each resultssimulation and of simuFM tolationof reach octorotor results the convergence. isofshown FM of octorotor in Figure is8. shown in Figure 8. It can be seen that the simulation results are slightly higher than the experiment, with an error of about 6%, which may be 0.37the result of the introduced CP in experiments and the extra validation of CP for each simulation to reach the convergence. 0.36

0.35 0.37

0.34 0.36

0.33 0.35 FM 0.32 0.34 Experiment 0.31 Simulation 0.33 FM 0.300.32 Experiment 0.290.31 Simulation 1.0 1.2 1.4 1.6 1.8 0.30 Spacing ratio

0.29 FigureFigure 8. Comparison1.0 between between 1.2 experiment experimental 1.4al and and1.6 simulation simulation 1.8 results. results. Spacing ratio It can be seen that the simulation results are slightly higher than the experiment, with an error of 4.2. Simulation Results about 6%, which mayFigure be the 8. result Comparison of the between introduced experimentCP inal experiments and simulation and results. the extra validation of CP for eachThe simulation velocity distribution to reach the between convergence. adjacent rotors with different rotor spacing is shown in Figure 9. 4.2. Simulation Results 4.2. Simulation Results The velocity distribution between adjacent rotors with different rotor spacing is shown in Figure 9. The velocity distribution between adjacent rotors with diﬀerent rotor spacing is shown in Figure9.

(a) (b) (c)

(d) (e)

(d) (e) Figure 9. Velocity distribution. (a) L/D = 1.8; (b) L/D = 1.6; (c) L/D = 1.4; (d) L/D = 1.2; (e) L/D = 1.0.

FigureFigure 9. Velocity 9. Velocity distribution. distribution. (a ()aL) /LD/D= =1.8; 1.8; ( b(b))L L//DD= = 1.6; ( c)) L//DD == 1.4;1.4; (d (d) )LL/D/D = =1.2;1.2; (e) ( eL)/DL/ D= 1.0.= 1.0.

Processes 2020, 8, x FOR PEER REVIEW 9 of 12 Processes 2020, 8, x 1364 FOR PEER REVIEW 9 of 12 According to Figure 9, it is not difficult to find that rotor wake began to attract each other as the According to Figure 9, it is not difficult to find that rotor wake began to attract each other as the rotor Accordingspacing was to reduced. Figure9, itSince is not the di wakefficult of to each find ro thattor rotor is affected wake beganby the towake attract of the each two other adjacent as the rotor spacing was reduced. Since the wake of each rotor is affected by the wake of the two adjacent rotors,rotor spacing the wake was of reduced.the rotor shows Since thethe wakephenomenon of each rotorof inward is aff ectedcontraction by the which wake may of the make two the adjacent rotor rotors, the wake of the rotor shows the phenomenon of inward contraction which may make the rotor unstablerotors, the and wake affect of thethe rotorpower shows consumption the phenomenon of the rotor. of inward It also contraction can be found which that maythe vertical make the vortex rotor unstable and affect the power consumption of the rotor. It also can be found that the vertical vortex belowunstable the and side a ffofect the the rotor power slowly consumption moves down of theas the rotor. rotor It alsospacing can bedecreases. found that In addition, the vertical the vortexwake below the side of the rotor slowly moves down as the rotor spacing decreases. In addition, the wake ofbelow 1.2 and the side1.0 ofappears the rotor to slowlybe deeper moves than down other as thespacing rotor ratios, spacing which decreases. may Inmake addition, the rotors the wake more of of 1.2 and 1.0 appears to be deeper than other spacing ratios, which may make the rotors more susceptible1.2 and 1.0 appearsto ground to beeffects. deeper than other spacing ratios, which may make the rotors more susceptible susceptible to ground effects. to groundThe vortices effects. distribution between adjacent rotors with different rotor spacing is shown in Figure The vortices distribution between adjacent rotors with different rotor spacing is shown in Figure 10. The vortices distribution between adjacent rotors with different rotor spacing is shown in Figure 10. 10.

(a) (b) (c) (a) (b) (c) Figure 10. Vortices distribution. (a) L/D = 1.8; (b) L/D = 1.4; (c) L/D = 1.0. Figure 10.10. Vortices distribution.distribution. (a)) L//DD == 1.8; ( b) L/D = 1.4;1.4; ( (cc)) LL//D = 1.0.1.0. Figure 10 shows that the tip vortices and root vortices also attract each other and with a decrease in rotorFigure spacing, 10 shows the attraction that the tip between vortices vortices the and vortices root root vortices becomes also more attract and each more other intense. and with with a a decrease decrease inin rotor rotorThe spacing, pressure the distribution attraction between around the the rotor vortices tips becomes with different more andandrotor moremore spacing intense.intense. is shown in Figure 11. The pressure distributiondistribution aroundaround thethe rotor rotor tips tips with with di differentﬀerent rotor rotor spacing spacing is shownis shown in Figurein Figure 11 . 11.

180 60 180 L/D=1.0 160 60 L/D=1.4 30 L/D=1.0 160 L/D=1.8 140 L/D=1.4 30 0 L/D=1.8 lower surface-1.0 120140 0 upper surface-1.0 -30 lower surface-1.0 120 lower surface-1.4 100 upperupper surface-1.4surface-1.0 -30 lowerlower surface-1.8surface-1.4 100 -60 80 upperupper surface-1.8surface-1.4 Pressure (Pa) -60 lower surface-1.8 80 -90 upper surface-1.8 60 Pressure (Pa)

Pressure difference (Pa) difference Pressure -90 -120 4060 Pressure difference (Pa) difference Pressure -120 40 -150 20 0.0 0.2 0.4 0.6 0.8 1.0 0.00.20.40.60.81.0 -150 20 0.0 0.2 0.4y/c 0.6 0.8 1.0 0.00.20.40.60.81.0y/c y/c (a) y/c (b) (a) (b) FigureFigure 11.11. PressurePressure distribution. distribution. (a )(a Pressure) Pressure diff erencedifference between between upper upper and lower and surface;lower surface; (b) Pressure (b) Figure 11. Pressure distribution. (a) Pressure difference between upper and lower surface; (b) Pressuredistribution distribution of upper of and upper lower and surface. lower surface. Pressure distribution of upper and lower surface. AsAs can can be be seen seen from from Figure Figure 11a,11a, the the pressure pressure difference difference between the upper and lower surface surface at at thethe blade bladeAs can tip tip be is is seen intended from Figureto decrease 11a, the with pressure a decrease difference in rotor between spacing. the It It upper means means and a a smaller smallerlower surface thrust thrust atis is obtainedtheobtained blade at attip smaller smaller is intended spacing. spacing. to decreaseFigure Figure 11b 11 withb shows shows a decrease that that the the in rotor rotorrotor spacing spacingspacing. has has It ameans a significant significant a smaller effect effect thrust on on the the is pressureobtained on at smallerthe upper spacing. surface Figure of of the 11brotor shows tip, but that when the rotorthe spacing spacing is is has too asmall significant (such (such as aseffect L//D on= 1.0), 1.0),the thepressurethe pressure pressure on theon the upper lower surface surface of theis also rotor affected aff tip,ected but in when this case. the spacing is too small (such as L/D = 1.0), the pressureTheThe streamline streamline on the lowerdistribution surface is is shown also affected in Figure in this1212.. case. The streamline inward contraction distribution of the is rotorshown wake in Figure at 1.2 and12. 1.0 can be clearly observed from Figure 12d,e which indicates that the thrust and power variations are related to the location and the shape of the vortex. The Q-criterion for the octorotor with different rotor spacing is shown in Figure 13. As can be seen in Figure 13, the wake of the rotor shows the phenomenon of inward contraction at L/D = 1.0.

(a) (b) (c) (a) (b) (c)

Processes 2020, 8, x FOR PEER REVIEW 9 of 12

According to Figure 9, it is not difficult to find that rotor wake began to attract each other as the rotor spacing was reduced. Since the wake of each rotor is affected by the wake of the two adjacent rotors, the wake of the rotor shows the phenomenon of inward contraction which may make the rotor unstable and affect the power consumption of the rotor. It also can be found that the vertical vortex below the side of the rotor slowly moves down as the rotor spacing decreases. In addition, the wake of 1.2 and 1.0 appears to be deeper than other spacing ratios, which may make the rotors more susceptible to ground effects. The vortices distribution between adjacent rotors with different rotor spacing is shown in Figure 10.

(a) (b) (c)

Figure 10. Vortices distribution. (a) L/D = 1.8; (b) L/D = 1.4; (c) L/D = 1.0.

Figure 10 shows that the tip vortices and root vortices also attract each other and with a decrease in rotor spacing, the attraction between the vortices becomes more and more intense. The pressure distribution around the rotor tips with different rotor spacing is shown in Figure 11.

180 60 160 L/D=1.0 L/D=1.4 30 140 L/D=1.8 0 lower surface-1.0 120 upper surface-1.0 -30 lower surface-1.4 100 upper surface-1.4 -60 lower surface-1.8 80 upper surface-1.8 Pressure (Pa) -90 60 Pressure difference (Pa) difference Pressure -120 40 -150 20 0.0 0.2 0.4 0.6 0.8 1.0 0.00.20.40.60.81.0 y/c y/c (a) (b)

Figure 11. Pressure distribution. (a) Pressure difference between upper and lower surface; (b) Pressure distribution of upper and lower surface.

As can be seen from Figure 11a, the pressure difference between the upper and lower surface at the blade tip is intended to decrease with a decrease in rotor spacing. It means a smaller thrust is obtained at smaller spacing. Figure 11b shows that the rotor spacing has a significant effect on the pressure on the upper surface of the rotor tip, but when the spacing is too small (such as L/D = 1.0), theProcesses pressure2020, 8 ,on 1364 the lower surface is also affected in this case. 10 of 12 The streamline distribution is shown in Figure 12.

Processes 2020, 8, x FOR PEER REVIEW 10 of 12

Processes 2020(,a 8) , x FOR PEER REVIEW (b) (c) 10 of 12

(d) (e)

Figure 12. Streamline for octorotor in hover. (a) L/D = 1.8; (b) L/D = 1.6; (c) L/D = 1.4; (d) L/D = 1.2; (e) L/D = 1.0.

The inward contraction of the rotor wake at 1.2 and 1.0 can be clearly observed from Figure 12d,e which indicates that the thrust and(d power) variations are related (e) to the location and the shape of the vortex.Figure 12. StreamlineFigure 12. for Streamline octorotor for in hover.octorotor (a) Lin/D hover.= 1.8; (a (b) )L/LD/D = =1.8;1.6; (b ()c L)/LD/D = =1.6;1.4; (c) ( dL)/DL /=D 1.4;= 1.2; (d) L/D = 1.2; (e) (eThe) L/D Q-criterion= 1.0. L/D = for 1.0. the octorotor with different rotor spacing is shown in Figure 13.

The inward contraction of the rotor wake at 1.2 and 1.0 can be clearly observed from Figure 12d,e which indicates that the thrust and power variations are related to the location and the shape of the vortex. The Q-criterion for the octorotor with different rotor spacing is shown in Figure 13.

(a) (b) (c)

FigureFigure 13. 13.Q-criterion Q-criterion for for octorotor octorotor in in hover. hover. (a ()aL) /LD/D= =1.8; 1.8; ( b(b) )L L/D/D= =1.4; 1.4; ( c(c))L L/D/D= =1.0. 1.0.

5. ConclusionsAs can be seen in Figure 13, the wake of the rotor shows the phenomenon of inward contraction

at L/ToD obtain= 1.0. the aerodynamic performance of a small octorotor with different rotor spacing, the small (a) (b) (c) rotor test bench measurements were carried out with CFD simulations. The conclusions are as follows: 5. Conclusions Figure 13. Q-criterion for octorotor in hover. (a) L/D = 1.8; (b) L/D = 1.4; (c) L/D = 1.0. 1. The aerodynamic performance of the rotors change with a change of rotor spacing, but this change To obtain the aerodynamic performance of a small octorotor with different rotor spacing, the is not linear, and therefore it cannot be simply judged that an increase or decrease in the spacing small rotor test benchAs can measurements be seen in Figure were 13, carried the wake out of with the CFDrotor simulations. shows the phenomenon The conclusions of inward are as contraction will have a consistent impact on the aerodynamic performance of the rotors. Further analysis is follows: at L/D = 1.0. needed to explore the reasons for the influence of rotor spacing on aerodynamic performance 1. andThe whetheraerodynamic5. Conclusions or not performance there is a law of that the can rotors be expressed change with mathematically. a change of Nevertheless,rotor spacing, through but this experiments,change is not we linear, found and that thereforeFM and itPL cannotat L/D be= si1.8mply have judged obvious that advantages an increase as or compared decrease in with the To obtain the aerodynamic performance of a small octorotor with different rotor spacing, the otherspacing spacing will have ratio, a which consistent can be impact regarded on the as theaerodynamic best spacing performance ratio under of the the current rotors. working Further small rotor test bench measurements were carried out with CFD simulations. The conclusions are as condition,analysis is while neededL/D to= explore1.0 obviously the reasons has a greatfor the negative influence impact of rotor on thespacing overall on aerodynamic aerodynamic follows: performanceperformance dueand to whether its too small or spacing.not there is a law that can be expressed mathematically. 2. AsNevertheless, compared1. The withthrough aerodynamic eight experiments, single performance rotors, we for found a of quadrotor the that rotors FM and change and hex-rotor PL with at with La/ Dchange the= 1.8 same ofhave rotor rotor obvious spacing, size, but this theadvantagesFM of octorotor changeas compared is shows not linear, with a higher other and value.therefore spacing Especially, ratio,it cannot whichL be/D si=canmply1.8 be was judgedregarded proven that as toan the be increase thebest optimal spacing or decrease in the rotorratio spacingunder spacingthe with current better will working have aerodynamic a consistentcondition, performance. whileimpact L /onD The = the 1.0 configuration aerodynamicobviously has of performance a the great octorotor negative of helps theimpact rotors. to Further increaseon the overall theanalysis aerodynamic aerodynamic is needed performance performance to explore of thedue the rotors, toreasons its too but forsmall at thethe spacing. same influence time increasesof rotor thespacing total areaon aerodynamic 2. ofAs the compared aircraft,performance with resulting eight in singleand a higher whether rotors, cost. foror Therefore, anot qu adrotorthere it is isand necessarya hex-rotorlaw that to makewithcan thebe a tradeo sameexpressedff rotoron rotor mathematically.size, arrangementthe FM of octorotorNevertheless, and oversize shows ofthrough a the higher vehicle. experiments, value. Especially, we found L/D =that 1.8 wasFM provenand PL toat be L /theD = optimal 1.8 have obvious 3. Therotor numerical spacingadvantages with simulation better as aerodynamic resultscompared at Re with performance.= other0.79 spacing10 5Theshow configurationratio, that which the wake can of thebe of anregardedoctorotor octorotor helpsas the and to best spacing tip × theincrease vortices theratio ofaerodynamic wake under attract the performance current each other.working of Moreover,the condition, rotors, but the while at attraction the L/ sameD = 1.0 becomestime obviously increases more has the obviousa great total negativearea as impact theof the rotor aircraft, spacingon theresulting decreases, overall in aerodynamic a whichhigher may cost. performance adversely Therefore, a ffitdueect is thetonecessary its aerodynamic too small to make spacing. performance a tradeoff on of rotor the arrangement2. As and compared oversize with of the eight vehicle. single rotors, for a quadrotor and hex-rotor with the same rotor size, 3. The numericalthe simulationFM of octorotor results shows at Re tipa =higher 0.79 × value.105 show Especially, that the wakeL/D = of1.8 an was octorotor proven and to bethe the optimal vortices of wakerotor attractspacing each with other. better Moreover, aerodynamic the attractionperformance. becomes The configuration more obvious of as the the octorotor rotor helps to spacing decreases,increase which the aerodynamic may adversely performance affect the of aerodynamicthe rotors, but performance at the same time of the increases rotor. Athe total area decrease in ofrotor the spacingaircraft, willresulting also affect in a higher the pressure cost. Therefore, difference it between is necessary the upper to make and a lowertradeoff on rotor surfaces of thearrangement rotor tips. and When oversize the rotor of thespacing vehicle. is too small, the pressure difference is sharply reduced,3. thusThe numericalaffecting the simulation thrust generated.results at Re Futuretip = 0.79 work× 105 showshould that attempt the wake to of obtain an octorotor an and the vortices of wake attract each other. Moreover, the attraction becomes more obvious as the rotor spacing decreases, which may adversely affect the aerodynamic performance of the rotor. A decrease in rotor spacing will also affect the pressure difference between the upper and lower surfaces of the rotor tips. When the rotor spacing is too small, the pressure difference is sharply reduced, thus affecting the thrust generated. Future work should attempt to obtain an

Processes 2020, 8, 1364 11 of 12

rotor. A decrease in rotor spacing will also affect the pressure difference between the upper and lower surfaces of the rotor tips. When the rotor spacing is too small, the pressure difference is sharply reduced, thus affecting the thrust generated. Future work should attempt to obtain an aerodynamic model that considers rotor interference to amend the conventional control theory with application in an octorotor with tilted rotors or wind disturbance.

Author Contributions: Y.L. carried out experiments, acquired the funding, and analyzed the results; Y.H. wrote the manuscript with assistance of Y.L.; H.W. performed a new set of simulations. All authors have read and agreed to the published version of the manuscript. Funding: This research was supported by the National Nature Science Foundation of China (grant no. 51505087), the Fuzhou University Jinjiang Science and Education Park (no. 2019-JJFDKY-59) and the Fujian Provincial Industrial Robot Basic Component Technology Research and Development Center (2014H21010011). Acknowledgments: The author thanks the Key Laboratory of Fluid Power and Intelligent Electro-Hydraulic Control (Fuzhou University), the Fujian Province University, and the Fuzhou University Jinjiang Science and Education Park for applying the experimental field. Conflicts of Interest: The authors declare no conflict of interest.

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