applied sciences
Article Aerodynamic Characteristics of Different Airfoils under Varied Turbulence Intensities at Low Reynolds Numbers
Yang Zhang , Zhou Zhou *, Kelei Wang and Xu Li
College of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China; [email protected] (Y.Z.); [email protected] (K.W.); [email protected] (X.L.) * Correspondence: [email protected]
Received: 17 December 2019; Accepted: 14 February 2020; Published: 2 March 2020
Featured Application: The study of airfoil affected by the unsteady jet flow of turboelectric distributed propulsion aircraft was conducted, which lays a good foundation for future design of turboelectric distributed propulsion (TeDP) unmanned aerial vehicles (UAVs).
Abstract: A numerical study was conducted on the influence of turbulence intensity and Reynolds number on the mean topology and transition characteristics of flow separation to provide better understanding of the unsteady jet flow of turboelectric distributed propulsion (TeDP) aircraft. By solving unsteady Reynolds averaged Navier-Stokes (URANS) equation based on C-type structural mesh and γ Ref transition model, the aerodynamic characteristics of the NACA0012 airfoil at − θt different turbulence intensities was calculated and compared with the experimental results, which verifies the reliability of the numerical method. Then, the effects of varied low Reynolds numbers and turbulence intensities on the aerodynamic performance of NACA0012 and SD7037 were investigated. The results show that higher turbulence intensity or Reynolds number leads to more stable airfoil aerodynamic performance, larger stalling angle, and earlier transition with a different mechanism. The generation and evolution of the laminar separation bubble (LSB) are closely related to Reynolds number, and it would change the effective shape of the airfoil, having a big influence on the airfoil’s aerodynamic characteristics. Compared with the symmetrical airfoil, the low-Reynolds-number airfoil can delay the occurrence of flow separation and produce more lift in the same conditions, which provides guidance for further airfoil design under TeDP jet flow.
Keywords: turboelectric distributed propulsion; low Reynolds number; turbulence intensity; laminar separation bubble; stall
1. Introduction The research over the last several years on the fixed-wing unmanned aerial vehicles (UAVs) with turboelectric distributed propulsion (TeDP) has attracted much attention. The most representative ones are X-57, ESAero, GL-10, N3-X, E-airbus, and many other models [1,2]. The TeDP system is used to provide lift when UAVs take off. Due to the driving of the distributed propulsion to the air, the flow behind the propulsion system grows extremely complex, which is not only accelerated, but also with strong turbulence. Meanwhile, the characteristic Reynolds number of the wing becomes ultra low because the freestream velocity is almost zero. Owing to the influence of the turbulence and low Reynolds number, the three-dimensional effect of the wing becomes more complicated, which means the wing would encounter the coupling of up and down wash flow, flow separation, laminar separation bubble, spanwise vortex and other phenomena [3–6].
Appl. Sci. 2020, 10, 1706; doi:10.3390/app10051706 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 1706 2 of 19
Different from the laminar flow in which the fluid elements keep parallel to each other, the turbulent flow makes the fluid elements in the irregular vortex motion, and the mixing of different size eddies causes strong exchange and transmission of energy and heat, rapid dissipation of mechanical energy [7,8]. Turbulent flow is three-dimensional, rotational, intermittent, highly disordered, diffusive and dissipative. The actual modes of turbulence are eddies and high-vorticity regions, so that turbulence is often described by eddy viscosity as a local property of the fluid [9]. Generally, it is considered that the turbulence intensity less than or equal to 1% is low-intensity turbulence, and the turbulence intensity greater than 10% is high-intensity turbulence. In the wind tunnel experiment, the turbulence intensity of the inflow is usually within 3%, but in the practical application, the turbulence intensity near the propulsion system is often more than 5%. When the flow is affected by a small fan’s wake and atmospheric turbulence, the turbulence intensity could usually be greater than 10% [10]. Due to the existence of a large number of mixed jets in the combustion chamber and complex cooling structure in the combustor liner, the turbulence intensity at the outlet of the aeroengine could be 15%–20% [11]. Therefore, in the face of the complex jet flow behind the UAV with TeDP, it is very important to study the aerodynamic characteristics of the two-dimensional airfoil under varied turbulence intensities and low Reynolds numbers (Re < 5 105). × Under a low Reynolds number, the current study of turbulence intensity mainly focuses on the flow near a flat plate. Gramespacher [12] carried out experiments to study the influence of flow homogeneity and isotropy, decay of turbulent kinetic energy, energy spectra, and length scales. Grzelak [13] investigated the isotropy and homogeneity of turbulence through skewness and kurtosis of the flow velocity distribution function and transverse variation. He also studied the impact of turbulence intensity on bypass laminar–turbulent transition parameters on a flat plate through experiments. Hancock [14] confirmed an appreciably nonlinear dependence of the skin-friction coefficient and other boundary layer parameters on RMS freestream turbulence intensity. Hiller [15] found that the mean flow-field responds strongly to turbulence intensity but with little effect of integral scale, and fluctuating pressures depend strongly upon both intensity and scale. Fransson [16] and Jacobs [17] observed the formation of streamwise oriented streaks in the separated shear layer, which significantly altered the flat plate boundary-layer transition under high levels of turbulence intensity. Marxen [18] analyzed the transition mechanism by observing the development of small disturbances and their role in the final breakdown to turbulence through direct numerical simulation (DNS). McAuliffe [19] conducted a numerical simulation of transition under low and high disturbance. The study examines the role of the velocity profile shape on the instability characteristics and the nature of the large-scale vortical structures shed downstream of the bubble and enables identification of the structure of the instability mechanism and the characteristic structure of the resultant turbulent spots. The research on the effect of turbulence intensity on airfoil is mostly concentrated on the turbine blade and low-speed airfoil. Lengani [10] found that the free-stream turbulence intensity modify the transition and separation processes of the suction side boundary layer of a highly loaded low pressure turbine blade through experiment. The stall characteristics of airfoil S1223 has been investigated by Cao [20] at low Reynolds numbers, implying that the smaller integral length under 4.1% turbulence intensity delays the boundary layer separation on the suction surface. Mistf [21] conducted an experiment of NACA0015 immersed in two grid generated homogenous flows. Istvan [22,23] investigated NACA0018 under varied Reynolds numbers and turbulence intensities to find that increasing freestream turbulence intensity results in earlier transition and reattachment, contributing to an overall decrease in separation bubble length. Bryan [24] established an extensive database of surface oil flow measurements of seven airfoils that represents a wide range in behavior at low Reynolds numbers. Wang and Li [25,26] carried out an experiment on NACA0012 under varied turbulence intensities at Re =5,300 to validate their numerical simulation. Arunvinthan [27] studied the aerodynamic characteristics of unsymmetrical airfoil at various turbulence intensities through experiments and found that the lift coefficient increases with the increase of turbulence intensity. The results also reveal that the flow featuring turbulence can effectively delay the stall characteristics Appl. Sci. 2020, 10, 1706 3 of 19 of an airfoil by attaching the flow over the airfoil for an ex-tended region. The influence of freestream turbulence intensity (FSTI) level on the structure and dynamic properties of a laminar separation bubble has been experimentally studied by Simoni [28]. He concluded that the bubble length and height reduction at a high FSTI level with a fixed Reynolds number are due to the higher amplitude of velocity fluctuations penetrating into the separating boundary layer. Conversely, the Reynolds number significantly influences the time-mean boundary layer structure at separation. The existing research on the influence of the turbulence intensity on airfoils have been conducted with Reynolds numbers between 100,000 and 1200,000, but the work under 100,000 Reynolds number is lacking. Meanwhile the TeDP UAV is a new topic, which brings about new problems in airfoil design. It is necessary to carry out further research on aerodynamic performance of airfoil in the flow with great changes of Reynolds number and turbulence intensity. Therefore, facing the unsteady jet flow generated by the TeDP system during taking off, the aerodynamic performance of airfoil under varied Reynolds numbers and turbulence intensities is studied by using the commercial software FLUENT based on the computational fluid dynamics (CFD) method. The numerical method applied in this paper is verified by comparing the pressure distribution, the lift and drag coefficient of the NACA0012 airfoil with different turbulence intensities and Reynolds numbers. The effects of turbulence intensity and Reynolds number on the aerodynamic performance of airfoil and flow field characteristics are studied. The mechanisms of earlier transition in the boundary layer, the relationship between the evolution of laminar separation bubble and Reynolds number are presented.
2. Numerical Approach
2.1. Estimation Method of Turbulence Intensity Turbulence intensity (Tu) is a physical quantity to measure the degree of irregular motion of fluid element. Turbulence intensity is defined as the ratio of the rms of fluctuating velocity u’ to average velocity U(Equation (1)) q u 2 Tu = 0 (1) U In turbulent flow, the mean values of velocity and pressure are easy to observe, while the fluctuating velocity can be measured by precise hot wire anemometer, laser velocimeter and particle image velocimetry. The turbulence energy is mainly concentrated in the large-scale eddy structure, which is related to the turbulence length scale l. The characteristic length of turbulence depends on the geometric length and has a decisive influence on the development of turbulence. If the flow at the entrance is restricted by the wall and has a turbulent boundary layer, the turbulent length scale can be calculated by l = 0.4δ99%, where the δ99% is the thickness of boundary layer. As for the flow affected by the inlet grid, the turbulence length scale is approximately equal to the grid aperture, namely l d.[6,21]. ≈ RT is the ratio of turbulence viscosity to laminar viscosity, which is directly proportional to the turbulent Reynolds number. In the high-Reynolds-number boundary layer, shear layer and fully developed pipe flow, the turbulence viscosity ratio is large, about 100–1000. However, in most free flow boundary layers, the turbulence viscosity ratio is quite small, usually 1–10. It is observed in a relative static wind tunnel that the turbulent flow behind the grid of the wind tunnel is steady, and its intensity is continuously attenuated along the flow direction from the inlet of the experimental section. According to the reference [29], the relationship between the turbulence attenuation and the increase of flow direction distance can be described as follows:
2 ! β∗/2β Tuinlet − Tu = Tuinlet 1 + Rex1.5β (2) RT,inlet Appl. Sci. 2020, 10, 1706 4 of 19
In the numerical simulation, the attenuation of turbulence intensity can be more directly reflected by the turbulent dissipation rate ε (Equation (3)).
k3/2 ε = β 3/4 (3) ∗ l where k is turbulent kinetic energy, β and β∗ are the empirical constants in the turbulence model. The values are β = 0.0828, β* = 0.09.
2.2. γ Ref Transition Model − θt The γ Ref transition model is based on the local variables of flow field proposed by Langtry and − θt Menter, in which the intermittence factor γ and the transition momentum thickness Reynolds number Refθt are added to construct the transport equations. The γ is used to depict the flow characteristics of the transition region, which represents the probability of turbulence at a point in flow field, and the value range is 0 γ 1. Ref is used to control the generation of intermittence factors and to form ≤ ≤ θt a criterion for predicting the starting position of transition. Transport equation of γ is:
" ! # ∂(ργ) ∂ ρUjγ ∂ µj ∂γ + = Pγ1 Eγ1 + Pγ2 Eγ2 + µ + (4) ∂t ∂xj − − ∂xj σj ∂xj
Transition source term and fracture/laminar fluidization source term are defined as follows:
Cγ3 Pγ1 = Ca1FlengthρS[γFonset] (5)
Eγ1 = Ce1Pγ1γ (6)
Pγ2 = Ca2ρΩγFturb (7)
Eγ2 = Ce2Pγ2γ (8) where S is strain rate, Flength is the empirical correlation for controlling the length of transition region, Ω is vorticity, the constant terms are Ca1 = 2, Ce1 = 1, Ca2 = 0.06, Ce2 = 50, Cγ3 = 0.5. The vorticity Reynolds number is defined as:
ρy2S Rev = (9) µ
The other parameters are as below: ρk R = (10) T µω
Rev Fonset1 = (11) 2193Reθc 4 Fonset2 = min max Fonset1, Fonset , 2.0 (12) 3 ! RT Fonset = max 1 , 0 (13) 3 − 2.5
Fonset = max(Fonset Fonset , 0) (14) 2 − 3 4 ( RT ) Fturb = e− 4 (15) Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 20 Appl. Sci. 2020, 10, 1706 5 of 19
4 RT − Fe= 4 (15) The transport equation of γ Ref is: turb − θt The transport equation of γ -Reθt is: ∂ ρRef ∂ ρU Ref θt j θt ∂ ∂Refθt ∂∂ρρ+ = Pθt + σθt(µ + µt) (16) ()Reθθtt()U j Re ∂∂ Reθ ∂t +=++∂xj P ∂xjσμμ()∂t xj ∂∂θθttt ∂ ∂ (16) txjj x x j The source term is defined as: The source term is defined as: ρ Pθt = cθt ρ Reθt Refθt (1.0 Fθt) (17) =−−t ()θ () Pcθθttt Re θ t− Ret 1.0 F− θ t (17) The coupled equation with the shear stress transport (SST) flow model is: The coupled equation with the shear stress transport (SST) flow model is: " # ∂∂∂∂ ∂ ∂∂∂k ( ) k ** ()ρρρkkukGYS++=Γ+−+()ρujk = Γk + G∗k Y∗k + Sk (18) ∂∂∂t ∂xj jkkkk∂ ∂∂xj ∂xj − (18) txjjj xx
G∗k* ==γe f fGek (19) GGkeffk (19) Y = Y ∗k* =min max γγe f f , 0.1 , 1.0 k (20) YYkeffkmin() max() ,0.1 ,1.0 (20) Other parameters are defined by reference [30–32]. Other parameters are defined by reference [30–32]. 3. Validation of Numerical Simulation Method 3. Validation of Numerical Simulation Method The numerical calculation is based on unsteady Reynolds averaged Navier-Stokes (URANS) equationsThe numerical coupling withcalculation the γ Reisf basedθt transition on unstea model.dy TheReynolds semi-implicit averaged method Navier-Stokes for pressure-linked (URANS) − equations coupling consistent with (SIMPLEC the γ -Re [θ33t , transition34]) scheme model. was usedThe semi-implicit for the pressure-velocity method for pressure-linked coupling. The equationsdiscretized consistent momentum (SIMPLEC and pressure [33,34]) correction scheme equations was used are for solved the pressure-velocity implicitly, whereas coupling. the velocity The discretizedcorrection is momentum solved explicitly, and pressure thus resulting correction in a equa semi-implicittions are solved method. implicitly, Second orderwhereas upwind the velocity spatial correctiondiscretization is solved was used explicitly, for all variables,thus resulting in combination in a semi-implicit with the method. least square Second cell-based order upwind method spatial for the discretizationgradients. The was time used step for is determinedall variables, by in Strouhal combination number with (Sr the) (Equation least square (21)), cell-based which is method a similarity for thecriterion gradients. to characterize The timethe step unsteady is determined flow. by Strouhal number (Sr) (Equation (21)), which is a similarity criterion to characterize the unsteady flow. f c Sr = (21) Ufc Sr = (21) U where the f is the frequency of unsteady period of motion, c the chord length of airfoil, and U the Wherevelocity the of flow.f is the frequency of unsteady period of motion, c the chord length of airfoil, and U the velocityThe of generation flow. of computational mesh and boundary conditions are shown in Figure1. The computationalThe generation meshof computational is divided bymesh C-type and structuralboundary mesh.conditions The are radius shown of calculationin Figure 1. fieldThe computationalis 50 times of the mesh chord is divided length. by C-type structural mesh. The radius of calculation field is 50 times of the chord length.
(a) (b)
Figure 1. Mesh and boundary conditions. (a) Mesh in farfield; (b) Mesh around airfoil. Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 20 Appl. Sci. 2020, 10, 1706 6 of 19
Figure 1. Mesh and boundary conditions. (a) Mesh in farfield; (b) Mesh around airfoil. 3.1. Validation of Pressure Distribution 3.1. Validation of pressure distribution Referring to reference [35], the numerical simulation of the NACA0012 airfoil at Reynolds number of 250,000Referring is carried to reference out. The [35], FSTI the in numerical experiment simu is Tulation= 0.58%. of the The NACA0012 angle of attackairfoil (AoA)at Reynolds of the number of 250,000 is carried out. The FSTI in experiment is Tu = 0.58%. The angle of attack (AoA) of airfoil is α = 4◦, and the chord length is c = 0.3048 m. The calculation condition is consistent with the experiment.the airfoil is Theα ₌ 4°, quantity and the of chord computational length is mesh c = 0.3048 is aboutm. The 100,000 calculation cells, and condition the first layeris consistent grid element with the experiment. The quantity of 5computational+ mesh is about 100,000 cells, and the first layer grid to wall distance is d1 = 2.03 10− c, y = 0.25. The inflow velocity is V = 11.982 m/s. × -5 + elementSolutions to wall are distance considered is d1 = su 2.03fficiently × 10 c, converged y = 0.25. The when inflow the order velocity of magnitude is V = 11.982 ofm/s the. residuals is low andSolutions remains are constant. considered Figure sufficiently2 shows theconverged assessment when between the order the of experiments magnitude andof the the residuals results of is thelow CFD, and remains where the constant. CFD by Figure Counsil 2 representsshows the numericalassessment solution between calculated the experiments in reference and [the36]. results of the CFD, where the CFD by Counsil represents numerical solution calculated in reference [36].
Figure 2. Comparison of numerical calculation and experiment results of pressure distribution. CFD: Figure 2. Comparison of numerical calculation and experiment results of pressure distribution. computational fluid dynamics; EXP: experiment. CFD: computational fluid dynamics; EXP: experiment. Figure2 shows that, the numerical simulation of the pressure distribution fits well with the Figure 2 shows that, the numerical simulation of the pressure distribution fits well with the experiment result, and describes the separation and reattachment process well. In addition, the CFD experiment result, and describes the separation and reattachment process well. In addition, the CFD results are consistent with those given by Counsil. It shows that the calculation method is accurate to results are consistent with those given by Counsil. It shows that the calculation method is accurate to predict the transition process. predict the transition process. 3.2. Validation of Aerodynamic Force 3.2. Validation of aerodynamic force Referring to reference [25], the numerical simulation of the NACA0012 airfoil at ultra-low Reynolds Referring to reference [25], the numerical simulation of the NACA0012 airfoil at ultra-low number of 5,300 is carried out. The range of the angle of attack of the airfoil is α = 0◦–25◦, chord length ofReynolds airfoil is numberc = 0.1 m. of The5,300 experiment is carried isout. conducted The range in aof water the angle tunnel, of andattack the of water the airfoil flow velocity is α = 0°–25°, is U = 0.053chord m length/s. Because of airfoil the is experimental c = 0.1m. The velocity experiment of the is water conducted tunnel in is a too water small, tunnel, the incompressible and the water flow flow conditionvelocity is is U transformed = 0.053m/s into. Because low-speed the experimental incompressible velocity air flow of according the water to thetunnel criterion is too of small, Reynolds the similarity.incompressible The size flow of condition the airfoil is is transformed scaled to 1/40 into of the low-speed original size,incompressible namely c’ = air0.0025 flow m. according The inflow to velocitythe criterion of air of inlet Reynolds boundary similarity. is V = The30.96 size m/ s.of the airfoil is scaled to 1/40 of the original size, namely c’ = 0.0025In orderm. The to verify inflow the velocity influence of air of theinlet quality boundary of computation is V = 30.96m/s mesh,. five angles of attacks of the NACA0012In order airfoil to verify were the calculated influence and of the compared quality withof computation the experimental mesh, five values. angles Figure of attacks3 represents of the theNACA0012 assessment airfoil between were thecalculated experiments and compared and the results with ofthe the experimental CFD computations values. Figure with three 3 represents different meshes:the assessment 52,500 between (coarse), the 73,000 experiments (medium), and and the 95,000 results (fine) of the cells. CFD computations with three different meshes:The 52,500 results (coarse), of the mesh 73,000 dependency (medium), studyand 95,000 is shown (fine) in cells. Table 1. Exp represents the experiment results, R the ratio of errors between Fine and Exp. All lift coefficients converged monotonically for all angles of attack and the value of R is less than 0.15. As illustrated in Figure3, the numerical results obtained with the fine mesh predicted the experimental lift well. Therefore, this higher resolution mesh was used for the current computations. It should be noted that because the due to value of lift at 2◦ angle of attack is small, the error of the numerical calculation result is relatively large. The computational mesh contains 95,000 cells, and the first layer grid element to wall distance is d1 = 6.53 10 4c, y+ = 0.25. × − Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 20
Appl. Sci. 2020, 10, 1706 7 of 19 Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 20
Figure 3. Lift coefficient of numerical simulations versus experiment data of the NACA0012 airfoil.
The results of the mesh dependency study is shown in Table 1. Exp represents the experiment results, R the ratio of errors between Fine and Exp. All lift coefficients converged monotonically for all angles of attack and the value of R is less than 0.15. As illustrated in Figure 3, the numerical results obtained with the fine mesh predicted the experimental lift well. Therefore, this higher resolution mesh was used for the current computations. It should be noted that because the due to value of lift at 2° angle of attack is small, the error of the numerical calculation result is relatively large. The Figure 3. Lift coefficient of numerical simulations versus experiment data of the NACA0012 airfoil. computationalFigure 3. Lift mesh coefficient contains of 95,000numerical cells, simulations and the first vers uslayer experiment grid element data of to the wall NACA0012 distance airfoil. is d1 = 6.53 × 10-4c,Table y+ = 1.0.25Results. of the mesh independency study. AOA: angle of attack; R: ratio of errors between Fine Theand Exp.results of the mesh dependency study is shown in Table 1. Exp represents the experiment results,Table R the 1. Resultsratio of of errors the mesh between independency Fine and study. Exp. AOA: All lift angle coefficients of attack; R:converged ratio of errors monotonically between for all angles of attack and the AOAvalue of Coarse R is less Fine Mediumthan and 0.15. Exp. As Fine illustrated Exp in Figure R 3, the numerical results obtained with the fine mesh2 predicted 0.1324 the experiment 0.1256 0.1123al lift well.0.098 Therefore, 0.146 this higher resolution AOA Coarse 5 0.3276Medium 0.3207 0.2950Fine0.282 0.046 Exp R mesh was2 used for the0.1324 current computations.0.1256 It should be noted0.1123 that because 0.098 the due to value 0.146 of lift at 2° angle of attack is small,8 the 0.6323error of the 0.6218 numerical 0.6224 calculation0.612 0.017result is relatively large. The 5 0.3276 10 0.73140.3207 0.7421 0.75070.29500.785 0.044 0.282 0.046 computational8 mesh0.6323 contains 12 95,000 0.7231 cells,0.6218 and 0.7748 the first layer 0.78930.6224 grid0.856 element 0.078 to 0.612 wall distance 0.017is d1 = 6.53 × 10-4c,10 y + = 0.25. 0.7314 0.7421 0.7507 0.785 0.044 12 0.7231 0.7748 0.7893 0.856 0.078 A definite curve of the decay law of experimental turbulence intensity at Tu = 6% is given in ATable definite 1. Results curve of of the the mesh decay independency law of experimental study. AOA: turbulence angle of attack; intensity R: ratio at of Tu errors = 6% between is given in reference [25], as is shown in Figure4a. TheFine range and between Exp. airfoil leading edge and trailing edge is referenceX/M = 14–16. [25], Aas decay is shown law in of Figure turbulence 4a. The intensity range between curve is fittedairfoil byleading changing edge turbulence and trailing scale edge and is X/Mturbulent=AOA 14–16. dissipation A decay Coarse rate law in of numerical turbulence calculation Medium intensity and curve is shown is fitted Fine in Figureby changing4b, where Exp turbulence the range scale between R and 2 0.1324 0.1256 0.1123 0.098 0.146 turbulentairfoil leading dissipation edge and rate trailing in numerical edge is X calculation= 0.0325– and0.03. is shown in Figure 4b, where the range between5 airfoil leading 0.3276 edge and trailing 0.3207 edge− is X = -0.0325− 0.2950 – ₋0.03. 0.282 0.046 8 0.6323 0.6218 0.6224 0.612 0.017 10 0.7314 0.7421 0.7507 0.785 0.044 12 0.7231 0.7748 0.7893 0.856 0.078
A definite curve of the decay law of experimental turbulence intensity at Tu = 6% is given in reference [25], as is shown in Figure 4a. The range between airfoil leading edge and trailing edge is X/M = 14–16. A decay law of turbulence intensity curve is fitted by changing turbulence scale and turbulent dissipation rate in numerical calculation and is shown in Figure 4b, where the range between airfoil leading edge and trailing edge is X = -0.0325 – ₋0.03.
(a) (b)
Figure 4. Decay law of turbulence intensity along the flow direction. (a) Turbulence intensity change in experiment; (b) Turbulence intensity change in numerical simulation.
The comparison between the numerical and experimental results of different turbulence intensities is depicted in Figure5. Figure5a indicates that the lift coe fficient fits well within the angle of attack of 10◦ at Tu = 6%. As the angle of attack increases, there is no definite stall phenomenon at α = 12◦–15◦, which is slightly different from the experimental results. As a result of the lack of corresponding decay law of experimental turbulence(a) intensity at Tu = 0.6%, the calculation error is(b large.) Even so, the trends of the lift and drag coefficients are consistent with the experimental results. Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 20 Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 20 Figure 4. Decay law of turbulence intensity along the flow direction. (a) Turbulence intensity change Figure 4. Decay law of turbulence intensity along the flow direction. (a) Turbulence intensity change in experiment; (b) Turbulence intensity change in numerical simulation. in experiment; (b) Turbulence intensity change in numerical simulation. The comparison between the numerical and experimental results of different turbulence The comparison between the numerical and experimental results of different turbulence intensities is depicted in Figure 5. Figure 5a indicates that the lift coefficient fits well within the angle intensities is depicted in Figure 5. Figure 5a indicates that the lift coefficient fits well within the angle of attack of 10° at Tu = 6%. As the angle of attack increases, there is no definite stall phenomenon at of attack of 10° at Tu = 6%. As the angle of attack increases, there is no definite stall phenomenon at α = 12°–15°, which is slightly different from the experimental results. As a result of the lack of α = 12°–15°, which is slightly different from the experimental results. As a result of the lack of correspondingAppl. Sci. 2020, 10, decay 1706 law of experimental turbulence intensity at Tu = 0.6%, the calculation error8 of is 19 corresponding decay law of experimental turbulence intensity at Tu = 0.6%, the calculation error is large. Even so, the trends of the lift and drag coefficients are consistent with the experimental results. large. Even so, the trends of the lift and drag coefficients are consistent with the experimental results.
(a) (b) (a) (b)
Figure 5. Comparison of numerical calculation and experiment results. (a) CL vs α;(b) CD vs α. Figure 5. Comparison of numerical calculation and experiment results. (a) CL vs α; (b) CD vs α. Figure 5. Comparison of numerical calculation and experiment results. (a) CL vs α; (b) CD vs α. The airfoil characteristics are further analyzed in the following section. In this paper, the numerical The airfoil characteristics are further analyzed in the following section. In this paper, the simulationThe airfoil is implemented characteristics with are an unsteadyfurther analyzed method, butin the figuresfollowing such section. as the streamlineIn this paper, diagram, the numerical simulation is implemented with an unsteady method, but the figures such as the numericalturbulent kineticsimulation energy is diagram,implemented pressure with distribution an unsteady diagram, method, friction but the drag figures diagram such and as so the on, streamline diagram, turbulent kinetic energy diagram, pressure distribution diagram, friction drag streamlinedeal with a diagram, time-averaged turbulent method. kinetic All energy numerical diagram, data arepressure the time-averaged distribution resultsdiagram, of 50friction time stepsdrag diagram and so on, deal with a time-averaged method. All numerical data are the time-averaged diagramafter convergence. and so on, Figure deal with6 shows a time-averaged the comparison method. of pressure All numerical distribution data of are the the airfoil time-averaged at di fferent results of 50 time steps after convergence. Figure 6 shows the comparison of pressure distribution of resultsturbulence of 50 intensities time steps and after angles convergence. of attack. Figure 6 shows the comparison of pressure distribution of the airfoil at different turbulence intensities and angles of attack. the airfoil at different turbulence intensities and angles of attack.
(a) (b) (c) (a) (b) (c) FigureFigure 6. 6. AirfoilAirfoil pressure pressure distribution distribution a affectedffected by by different different turbulence turbulence intensities intensities at at three three angles angles of of Figure 6. Airfoil pressure distribution affected by different turbulence intensities at three angles of attack.attack. ( (aa)) αα == 5°;5◦ (;(bb) )αα = =10°;10 ◦(;(c)c α) α= =15°.15 ◦. attack. (a) α = 5°; (b) α = 10°; (c) α = 15°.
TheThe pressure pressure distribution showsshows that:that: therethere areare few few di differencesfferences in in pressure pressure distributions distributions at αat= α5 =◦, The pressure distribution shows that: there are few differences in pressure distributions at α = 5°,and and the the overall overall trend trend of pressure of pressure distribution distribution is relatively is relatively approximate approximate (Figure 6(Figurea). As for6a). the As pressure for the 5°, and the overall trend of pressure distribution is relatively approximate (Figure 6a). As for the pressuredistribution distribution at Tu = 0.6%, at Tu the = upper 0.6%, and the lowerupper surface and lower pressure surface coeffi pressurecients tend coefficients to be consistent tend to about be pressure distribution at Tu = 0.6%, the upper and lower surface pressure coefficients tend to be consistent50%c, resulting about in50%c, the lossresulting of lift in contribution the loss of lift from contribution this position from to thethis trailing position edge. to the However, trailing edge. there consistent about 50%c, resulting in the loss of lift contribution from this position to the trailing edge. However,are significant there diarefferences significant in pressure differenc distributionses in pressure between distributionsTu = 6% between and Tu Tu= =0.6% 6% and at α Tu= 10 = ◦0.6%and However, there are significant differences in pressure distributions between Tu = 6% and Tu = 0.6% atα =α =15 10°◦ (Figure and α6 =b,c). 15° At(FigureTu = 6b,6%, 6c). the At pressure Tu = 6%, distribution the pressure changes distribution sharply changes for the sharply both angles for the of at α = 10° and α = 15° (Figure 6b, 6c). At Tu = 6%, the pressure distribution changes sharply for the bothattack. angles A pressure of attack. bulge A pressure is generated bulge at is about generated 20%c andat about 10%c 20%c respectively, and 10%c which respectively, is similar towhich that is of boththe classical angles of separation attack. A bubble, pressure and bulge is quite is generated different fromat about that 20%c of the and flow 10%c separation respectively, at high which angle ofis attack. At Tu = 0.6%, the premature separation of the flow results in a rapid attenuation of the suction peak near the leading edge of the airfoil, and the pressure coefficient near 5%c keeps almost constant until the trailing edge, which indicates that the high turbulence intensity has a certain inhibitory effect on the flow separation. A further comparison of turbulent kinetic energy and streamline around the airfoil corresponding to Tu = 6% and Tu = 0.6% is conducted in the following figures (Figures7 and8). The streamlines in the figures clearly reflect the aerodynamic characteristics of the flow field. Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 20 Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 20 similar to that of the classical separation bubble, and is quite different from that of the flow separation at high angle of attack. At Tu = 0.6%, the premature separation of the flow results in a rapid attenuation of the suction peak near the leading edge of the airfoil, and the pressure coefficient near 5%c keeps almost constant until the trailing edge, which indicates that the high turbulence intensity has a certain inhibitory effect on the flow separation. A further comparison of turbulent kinetic energy and streamline around the airfoil Appl. Sci. 2020, 10, 1706 9 of 19 corresponding to Tu = 6% and Tu = 0.6% is conducted in the following figures (Figures 7 and 8). The streamlines in the figures clearly reflect the aerodynamic characteristics of the flow field.
(a) (b) (c) Figure 7. Flow characteristic such as turbulent kinetic energy and streamline shape at Tu = 6%, (a) α Figure 7. Flow characteristic suchsuch as as turbulent turbulen kinetict kinetic energy energy and and streamline streamline shape shape at Tu at= Tu6%, = (6%,a) α (=a)5 α◦; = 5°; (b) α = 10°; (c) α = 15°. =(b 5°;) α (=b)10 α ◦=;( 10°;c) α (=c) 15α ◦=. 15°.
(a) (b) (c) Figure 8. Flow characteristic such as turbulent kinetic energy and streamline shape at Tu = 0.6%, (a) α Figure 8. 8. FlowFlow characteristic characteristic such such as asturbulen turbulentt kinetic kinetic energy energy and and streamline streamline shape shape at Tu at = Tu0.6%,= 0.6%,(a) α = 5°; (b) α = 10°; (c) α = 15°. =(a 5°;) α (=b)5 α◦;( =b 10°;) α =(c10) α◦ =;( 15°.c) α = 15◦. It can be seen that: At α = 5 and Tu = 6%, the flow separation only occurs near the trailing edge It can be seen that: At α = 5°and◦ Tu = 6%, the flow separation only occurs near the trailing edge of the airfoil, and the streamline adheres well at other positions; At α = 10 , the separation begins of the airfoil, and the streamline adheres well at other positions; At α = 10°, the◦ separation begins near near 20%c of the upper surface of the airfoil and reaches to the trailing edge. The topology of the 20%c of the upper surface of the airfoil and reaches to the trailing edge. The topology of the separation separation vortex is more similar to the characteristics of the classical laminar separation bubble (LSB) vortex is more similar to the characteristics of the classical laminar separation bubble (LSB) separation separation as mentioned earlier. With the increase of the angle of attack, the scale of the separation as mentioned earlier. With the increase of the ananglegle of attack, the scale of the separation vortex vortex becomes larger and the separation point is advanced, but the center of the separation vortex is becomes larger and the separation point is advanced, but the center of the separation vortex is still still within the chord range of the airfoil. When the turbulence intensity is 0.6%, the flow separation within the chord range of the airfoil. When the turbulence intensity is 0.6%, the flow separation region region expands as the angle of attack increases. At α = 5 , the flow separation occurs near 45%c of its expands as the angle of attack increases. At α = 5°, the flow◦ separation occurs near 45%c of its upper upper surface. At α = 15 , the streamline begins to separate near 5%c of the upper surface, and there is surface. At α = 15°, the streamline◦ begins to separate near 5%c of the upper surface, and there is no no reattachment after the flow separation. The center of the separation vortex is located outside the reattachment after the flow separation. The center of the separation vortex is located outside the chord of the airfoil, forming a typical high-attack-angle separation. chord of the airfoil, forming a typical high-attack-angle separation. The magnitude of turbulent kinetic energy represents the intensity of turbulence. When transition The magnitude of turbulent kinetic energy represents the intensity of turbulence. When occurs in the boundary layer, the turbulent kinetic energy would increase sharply. Comparing the transition occurs in the boundary layer, the turbulent kinetic energy would increase sharply. streamline and turbulent kinetic energy under two turbulence intensities, it can be found that when Comparing the streamline and turbulent kinetic energy under two turbulence intensities, it can be the airfoil is at the same angle of attack, the flow corresponding to the large turbulence intensity is found that when the airfoil is at the same angle of attack, the flow corresponding to the large more stable, and the flow separation area is smaller. This means that the larger turbulence intensity turbulence intensity is more stable, and the flow separation area is smaller. This means that the larger can inject the high energy from the freestream into the turbulent shear layer, and the fluid elements can turbulence intensity can inject the high energy from the freestream into the turbulent shear layer, and overcome some adverse pressure gradient to make the flow separation restrained. From the above, it can be seen that the numerical simulation method adopted in this paper is applicable to the calculation of complex flow under varied low Reynolds numbers and turbulence intensities, which meets the application of airfoil design under the jet flow of TeDP UAV. Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 20 theAppl. fluidSci. 2020 elements, 10, x FOR canPEER overcome REVIEW some adverse pressure gradient to make the flow separation10 of 20 restrained. the fluid elements can overcome some adverse pressure gradient to make the flow separation From the above, it can be seen that the numerical simulation method adopted in this paper is restrained. applicable to the calculation of complex flow under varied low Reynolds numbers and turbulence From the above, it can be seen that the numerical simulation method adopted in this paper is intensities, which meets the application of airfoil design under the jet flow of TeDP UAV. applicable to the calculation of complex flow under varied low Reynolds numbers and turbulence Appl. Sci. 2020, 10, 1706 10 of 19 4.intensities, Effect of whichTurbulence meets Intensitythe application on Airfoil of airfoil at Different design under Reynolds the jet Numbers flow of TeDP UAV. Considering the variability of the jet flow of TeDP aircraft affects the aerodynamic performance 4. Effect Effect of Turbulence IntensityIntensity onon AirfoilAirfoil atat DiDifferentfferent ReynoldsReynolds Numbers Numbers of the wing, the effect of turbulence intensity and Reynolds number on airfoil is studied in the Considering the variability of the jet flow of TeDP aircraft affects the aerodynamic performance followingConsidering section. the As variability stated earlier, of the there jet flow is quit of TeDPe a lot aircraft of research affects of the for aerodynamic Reynolds number performance between of of the wing, the effect of turbulence intensity and Reynolds number on airfoil is studied in the the100,000 wing, and the 1200,000. effect of turbulenceThus, Re1 = intensity26,500 and and Re Reynolds2 = 53,000 are number chosen on for airfoil further is studied research, inthe and following the state following section. As stated earlier, there is quite a lot of research of for Reynolds number between section.of Re3 = 212,000 As stated is earlier,calculated there as isa quitecomplement. a lot of researchIn addition, of for since Reynolds NACA0012 number is a between popular 100,000 symmetric and 100,000 and 1200,000. Thus, Re1 = 26,500 and Re2 = 53,000 are chosen for further research, and the state 1200,000.airfoil, the Thus, SD7037Re 1airfoil= 26,500 is selected and Re 2for= 53,000comparison. are chosen The SD7037 for further airfoil research, has a relative and the thickness state of Re of3 t/c= of Re3 = 212,000 is calculated as a complement. In addition, since NACA0012 is a popular symmetric 212,000= 9.20% isand calculated a relative as camber a complement. of f/c = 3.02%. In addition, It operates since at NACA0012 a low Reynolds is a popular number symmetric and it is favored airfoil, airfoil, the SD7037 airfoil is selected for comparison. The SD7037 airfoil has a relative thickness of t/c thefor SD7037R/C model airfoil sailplanes is selected because for comparison. of its working The SD7037lift range airfoil (the haslift range a relative over thickness the low ofdragt/c =region)9.20% = 9.20% and a relative camber of f/c = 3.02%. It operates at a low Reynolds number and it is favored andthat abegins relative near camber a CL of f0.2/c = and3.02%. extends It operates to near at C aL lowof 1.0 Reynolds where the number drag andbegins it is to favored increase for more R/C for R/C model sailplanes because of its working lift range (the lift range over the low drag region) modelrapidly sailplanes [37]. During because the ofcalculation, its working the lift rangeturbulence (the lift intensity range over at the lowleading drag edge region) of thatairfoils begins is that begins near a CL of 0.2 and extends to near CL of 1.0 where the drag begins to increase more nearguaranteed a CL of to 0.2 be and Tu = extends 6% and to Tu near = 0.6%.CL ofThe 1.0 lift where and drag thedrag characteristics begins to increaseare shown more in Figures rapidly 9 [and37]. rapidly [37]. During the calculation, the turbulence intensity at the leading edge of airfoils is During10. the calculation, the turbulence intensity at the leading edge of airfoils is guaranteed to be Tu = 6%guaranteed and Tu = to0.6%. be Tu The = 6% lift and and Tu drag = 0.6%. characteristics The lift and are drag shown characteristics in Figures9 areand shown 10. in Figures 9 and 10.
(a) (b)
(a) (b) Figure 9. Aerodynamic characteristics of NACA0012 at different Reynolds numbers and turbulence Figure 9. Aerodynamic characteristics of NACA0012 at different Reynolds numbers and turbulence intensities. (a) CL vs α; (b) CD vs α. intensities.Figure 9. Aerodynamic (a) CL vs α;( bcharacteristics) CD vs α. of NACA0012 at different Reynolds numbers and turbulence
intensities. (a) CL vs α; (b) CD vs α.
(a) (b)
Figure 10. Aerodynamic(a) characteristics of SD7037 at different Reynolds numbers(b) and turbulence intensities. (a) CL vs α;( b) CD vs α. Generally, the flow around airfoils is complex in the range of Re = 10,000–100,000. There may be laminar boundary layer, laminar separation, transition, turbulent boundary layer and turbulent separation. It can be seen from Figures9 and 10 that under Tu = 6% corresponding to states of Re1 = 26,500 and Re2 = 53,000, the lift coefficient increases linearly with small angle of attack. At Re2 = 53,000, the stalling angle of NACA0012 is 12◦, while that of SD7037 is 15◦. This shows that the SD7037 airfoil Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 20
Figure 10. Aerodynamic characteristics of SD7037 at different Reynolds numbers and turbulence
intensities. (a) CL vs α; (b) CD vs α.
Generally, the flow around airfoils is complex in the range of Re = 10,000–100,000. There may be laminar boundary layer, laminar separation, transition, turbulent boundary layer and turbulent separation. It can be seen from Figures 9 and 10 that under Tu = 6% corresponding to states of Re1 = 26,500 and Re2 = 53,000, the lift coefficient increases linearly with small angle of attack. At Re2 = 53,000, the stalling angle of NACA0012 is 12°, while that of SD7037 is 15°. This shows that the SD7037 airfoil has better lift characteristics. At Tu = 0.6%, the lift coefficient is evidently nonlinear and the stalling angle is smaller for both of the airfoils. At Re1 = 26,500, the stalling angle of both airfoils decreases to only 8°, and there is a sharp increase of drag around α = 10°. Figure 11 also indicates that the pressure dragAppl. Sci.of 2020the ,airfoil10, 1706 suddenly increases at α = 10°, which may be the result of the development 11of ofthe 19 flow separation with the increase of the angle of attack. At Re3 = 212,000, the lift coefficient of both airfoilshas better increases lift characteristics. further, and AttheTu stalling= 0.6%, ph theenomenon lift coeffi delays,cient is which evidently is more nonlinear evident and at theTu stalling= 0.6%. Notably, at α = 2° and α = 5°, the lift coefficient of the airfoil at Tu = 0.6% is bigger than that at Tu = angle is smaller for both of the airfoils. At Re1 = 26,500, the stalling angle of both airfoils decreases to 6%, which might have something to do with the generation of the LSB. only 8◦, and there is a sharp increase of drag around α = 10◦. Figure 11 also indicates that the pressure In the aspect of drag, Figure 11a (in which CD,p represents the coefficient of pressure drag, CD,f drag of the airfoil suddenly increases at α = 10◦, which may be the result of the development of the the coefficient of friction drag) indicates that the NACA0012 airfoil has a small pressure drag at small flow separation with the increase of the angle of attack. At Re3 = 212,000, the lift coefficient of both angleairfoils of increases attack. With further, the andangle the of stalling attack increasing phenomenon to 15°, delays, the whichairfoil isstalls more and evident the pressure at Tu = 0.6%.drag increases sharply at Tu = 0.6%. Besides, in comparison with a high level of turbulence intensity, the Notably, at α = 2◦ and α = 5◦, the lift coefficient of the airfoil at Tu = 0.6% is bigger than that at Tu = 6%, frictionalwhich might drag have is smaller something at Tu to = do 0.6%. with The the variation generation of of drag the LSB.characteristics of the SD7037 airfoil is similar to NACA0012 (Figure 11b).
(a) (b) Figure 11. The component of the drag coefficient of airfoils varies with the angle of attack at different Reynolds numbers and turbulence intensities. (a) NACA0012; (b) SD7037. Figure 11. The component of the drag coefficient of airfoils varies with the angle of attack at different Reynolds numbers and turbulence intensities. (a) NACA0012; (b) SD7037. In the aspect of drag, Figure 11a (in which CD,p represents the coefficient of pressure drag, CD,f the coefficient of friction drag) indicates that the NACA0012 airfoil has a small pressure drag at small angle Generally, as for a specific Reynolds number, the increasing freestream turbulence intensity of attack. With the angle of attack increasing to 15 , the airfoil stalls and the pressure drag increases results in a minor decrease in lift at small angle of◦ attack, whereas at pre-stall angle of attack and sharply at Tu = 0.6%. Besides, in comparison with a high level of turbulence intensity, the frictional higher turbulence intensity levels, lift increases and stall is delayed, as stated in [22]. Similarly, at a drag is smaller at Tu = 0.6%. The variation of drag characteristics of the SD7037 airfoil is similar to specific turbulence intensity, the increasing Reynolds number results in improvement of NACA0012 (Figure 11b). aerodynamic performance of airfoil, and the enhancement of the ability of the boundary layer to resist Generally, as for a specific Reynolds number, the increasing freestream turbulence intensity results the adverse pressure gradient. Compared with NACA0012, the lift characteristics of the SD7037 in a minor decrease in lift at small angle of attack, whereas at pre-stall angle of attack and higher airfoil are better, while the drag coefficient is slightly higher. Winslow [6] also concluded that below turbulence intensity levels, lift increases and stall is delayed, as stated in [22]. Similarly, at a specific the Reynolds number of 105, cambered airfoils have better lift and drag characteristics than thick turbulence intensity, the increasing Reynolds number results in improvement of aerodynamic conventional airfoils with rounded-leading edges. performance of airfoil, and the enhancement of the ability of the boundary layer to resist the adverse The differences of airfoil aerodynamic characteristics under the influence of different Reynolds pressure gradient. Compared with NACA0012, the lift characteristics of the SD7037 airfoil are better, numbers and turbulence intensities will be further analyzed in the following section. while the drag coefficient is slightly higher. Winslow [6] also concluded that below the Reynolds number of 105, cambered airfoils have better lift and drag characteristics than thick conventional 4.1. The Influence of turbulence intensity upon airfoils at Re1 = 26,500 airfoils with rounded-leading edges. The differences of airfoil aerodynamic characteristics under the influence of different Reynolds numbers and turbulence intensities will be further analyzed in the following section.
4.1. The Influence of Turbulence Intensity Upon Airfoils at Re1 = 26,500
At Re1 = 26,500, the aerodynamic characteristics of airfoils were analyzed at angles of attack of 5◦, 8◦ and 10◦. The pressure distribution and chordwise friction drag coefficient (Cf,X) of airfoils in varied turbulence intensities is shown in Figures 12 and 13. Analyzing the pressure coefficient and friction coefficient under different turbulence intensities, together with the details of the corresponding flow field (Figures 14–17), it can be seen that: Appl. Sci. 2020, 10, x FOR PEER REVIEW 12 of 20 Appl. Sci. 2020, 10, x FOR PEER REVIEW 12 of 20
At Re1 = 26,500, the aerodynamic characteristics of airfoils were analyzed at angles of attack of At Re1 = 26,500, the aerodynamic characteristics of airfoils were analyzed at angles of attack of Appl.5°, Sci.8° and2020 ,10°.10, 1706 The pressure distribution and chordwise friction drag coefficient (Cf,X) of airfoils12 in of 19 5°, 8° and 10°. The pressure distribution and chordwise friction drag coefficient (Cf,X) of airfoils in varied turbulence intensities is shown in Figures 12 and 13. varied turbulence intensities is shown in Figures 12 and 13.
(a) (b) (c) (a) (b) (c) Figure 12. Airfoil pressure distribution affected by different turbulence intensities at three angles of FigureFigure 12. 12.Airfoil Airfoil pressure pressure distribution distribution aaffffectedected by different different turbulence turbulence intensities intensities at at three three angles angles of of attack. (a) α = 5°; (b) α = 8°; (c) α = 10°. attack.attack. (a ()aα) α= =5 5°;◦;( (bb)) αα == 8°;8◦;( (cc)) αα == 10°.10◦ .
Appl. Sci. 2020, 10, x FOR PEER REVIEW 13 of 20 Appl. Sci. 2020, 10, x (FORa) PEER REVIEW (b) (c) 13 of 20 (a) (b) (c) distributionFigureFigure 13. 13. platformAirfoil Airfoil chordwise chordwise on the upperskin skinfriction surffrictionace drag dragof the coecoefficien twofficient airfoit aaffectedfflsected appears byby didifferent ffearlier.erent turbulenceturbulence The flow separation intensities at has distributionFigure 13. platform Airfoil chordwise on the upper skin surffrictionace dragof the coefficien two airfoit affectedls appears by different earlier. turbulenceThe flow separationintensities has the threecharacteristicsat three angles angles of attack. ofof attack.separation (a) (αa)= α5 =bubbles ;(5°;b ()bα) α= in=8 8°; terms;( c()c)α α = of=10 10°. pressure. distribution. the characteristicsat three angles of attack.separation (a) α =◦bubbles 5°; (b) α in=◦ 8°;terms (c) α of = 10°.pressure◦ distribution. Analyzing the pressure coefficient and friction coefficient under different turbulence intensities, Analyzing the pressure coefficient and friction coefficient under different turbulence intensities, together with the details of the corresponding flow field (Figures 14–17), it can be seen that: together with the details of the corresponding flow field (Figures 14–17), it can be seen that: At α = 5°, the surface pressure distribution curve of the NACA0012 airfoil is smooth at Tu = 6%, At α = 5°, the surface pressure distribution curve of the NACA0012 airfoil is smooth at Tu = 6%, indicating that the flow is stable and the streamline adheres well (Figure 12a, 14a). While the indicating that the flow is stable and the streamline adheres well (Figure 12a, 14a). While the boundary layer on the upper surface of SD7037 airfoil begins to separate at about 82%c and reattached boundary layer on the upper surface of SD7037 airfoil begins to separate at about 82%c and reattached near the trailing edge, forming a separation bubble (Figure 16a). However, because the separation near the trailing edge, forming a separation bubble (Figure 16a). However, because the separation bubble is small, the airfoil pressure distribution does not change significantly. At Tu = 0.6%, the bubble is small, the airfoil pressure distribution does not change significantly. At Tu = 0.6%, the pressure distribution of the NACA0012 airfoil around 30%–60%c on the upper surface forms a pressure distribution of the NACA0012 airfoil around 30%–60%c on the upper surface forms a pressure platform. The Cf,X becomes negative at 18%c, which indicates that the flow is separated pressure platform.(a) The Cf,X becomes negative at(b 18%c,) which indicates that the(c )flow is separated (Figures 13a and (15a).a) The streamline around NACA0012(b) wraps a slender eddy (duec) to the laminar (Figures 13a and 15a). The streamline around NACA0012 wraps a slender eddy due to the laminar separationFigure (Figure14. The NACA0012 15a). The SD7037 airfoil characteristics airfoil also expe such riencesas turbulent flow kinetic separation, energy butand thestreamline separation shape point separationFigureFigure 14. (Figure14.The The NACA0012 NACA0012 15a). The airfoilSD7037airfoil characteristics airfoil also expesuch riencesas as turbulent turbulent flow kinetic kineticseparation, energy energy butand and streamlinethe streamline separation shape shape point is slightlyat Tu =delayed, 0.6%; (a) atα =about 5°; (b )25%c α = 8°; (Figure (c) α = 10°.17a). is slightlyatatTu Tu= =0.6%;delayed, 0.6%; (a ()a)α atα= =about5 5°;;( (bb) )25%c αα == 8°;8 (Figure;( (cc)) αα == 10°. 17a).10 . When the angle of ◦attack of the◦ airfoils ◦increases to 8°, flow separation occurs near the trailing When the angle of attack of the airfoils increases to 8°, flow separation occurs near the trailing edge of the NACA0012 airfoil at Tu = 6%, and a separation bubble forms near the trailing edge of the edge of the NACA0012 airfoil at Tu = 6%, and a separation bubble forms near the trailing edge of the SD7037 airfoil (Figure 13b, 16b). At Tu = 0.6%, flow separation occurs near 4%c on the upper surface SD7037 airfoil (Figure 13b, 16b). At Tu = 0.6%, flow separation occurs near 4%c on the upper surface of NACA0012 airfoil, and the separation area extends to the trailing edge (Figure 15b). Similarly, flow of NACA0012 airfoil, and the separation area extends to the trailing edge (Figure 15b). Similarly, flow separation occurs near 14%c on the upper surface of SD7037 airfoil (Figure 17b). With the angle of separation occurs near 14%c on the upper surface of SD7037 airfoil (Figure 17b). With the angle of attack increasing to 10°, at Tu = 6%, a slender separation bubble is generated around 3%–16%c on the attack increasing to 10°, at Tu = 6%, a slender separation bubble is generated around 3%–16%c on the upper surface of the NACA0012 airfoil, and the flow separation area near the trailing edge is upper surface of the NACA0012 airfoil, and the flow separation area near the trailing edge is expanded (Figure 14c). The location of trailing edge separation bubble on the SD7037 airfoil is slightly expanded (Figure 14c). The location of trailing edge separation bubble on the SD7037 airfoil is slightly advanced, and a longer separation bubble is formed near 8%–20%c. At Tu = 0.6%, the pressure advanced, and a longer separation bubble is formed near 8%–20%c. At Tu = 0.6%, the pressure
(a) (b) (c) (a) (b) (c) FigureFigure 15. 15.The TheNACA0012 NACA0012 airfoilairfoil characteristics such such as as turbulent turbulent kinetic kinetic energy energy and and streamline streamline shape shape Figure 15. The NACA0012 airfoil characteristics such as turbulent kinetic energy and streamline shape atatTu Tu= =0.6%, 0.6%, ( a(a) )α α= = 55°;;( (b)) α = 8°;8 ;((cc)) αα == 10°.10 . at Tu = 0.6%, (a) α = 5°;◦ (b) α = 8°;◦ (c) α = 10°.◦
(a) (b) (c) (a) (b) (c) Figure 16. The SD7037 airfoil characteristic such as turbulent kinetic energy and streamline shape at Figure 16. The SD7037 airfoil characteristic such as turbulent kinetic energy and streamline shape at Tu = 6%, (a) α = 5°; (b) α = 8°; (c) α = 10°. Tu = 6%, (a) α = 5°; (b) α = 8°; (c) α = 10°. Appl. Sci. 2020, 10, x FOR PEER REVIEW 13 of 20
distribution platform on the upper surface of the two airfoils appears earlier. The flow separation has the characteristics of separation bubbles in terms of pressure distribution.
(a) (b) (c)
Figure 14. The NACA0012 airfoil characteristics such as turbulent kinetic energy and streamline shape at Tu = 0.6%; (a) α = 5°; (b) α = 8°; (c) α = 10°.
(a) (b) (c)
Figure 15. The NACA0012 airfoil characteristics such as turbulent kinetic energy and streamline shape Appl. Sci. 2020, 10, 1706 13 of 19 at Tu = 0.6%, (a) α = 5°; (b) α = 8°; (c) α = 10°.
(a) (b) (c)
FigureFigure 16. 16.The The SD7037 SD7037 airfoil airfoil characteristic characteristic such such as as turbulent turbulent kinetic kinetic energy energy andand streamlinestreamline shapeshape atatTu Appl. Sci. 2020, 10, x FOR PEER REVIEW 14 of 20 = Tu6%, = (6%,a) α (a=) 5α◦ =;( 5°;b) (αb=) α8 ◦=;( 8°;c) (αc)= α 10= 10°.◦.
(a) (b) (c)
FigureFigure 17. 17.The The SD7037 SD7037 airfoil airfoil characteristic characteristicsuch suchas asturbulent turbulent kinetickinetic energyenergy andand streamlinestreamline shapeshape atat Tu
=Tu0.6%, = 0.6%, (a) α (a=) α5◦ =;( 5°;b) (αb)= α8 =◦ ;(8°;c )(cα) =α 10= 10°.◦.
AtFromα = the5◦, theevolution surface of pressureflow separation distribution on the curve upper of surface the NACA0012 of the airfoils airfoil at Tu is = smooth 0.6% can at Tube = 6%,concluded indicating that that the the increasing flow is stableangle andof attack the streamline results in the adheres increase well of (Figures adverse 12 pressurea and 14 gradienta). While thearound boundary the trailing layer edge, on the contributing upper surface to the of separation SD7037 airfoil of the begins boundary to separate layer. Then at aboutthe separation 82%c and reattachedpoint moves near towards the trailing the leading edge, forming edge until a separation the complete bubble high-attack-angle (Figure 16a). separation, However, becauseand stall the separationhappens. However, bubble is the small, airfoil’s the airfoilaerodynamic pressure performa distributionnce improves does not and change the process significantly. of separation At Tu is = 0.6%,suppressed the pressure at Tu distribution= 6%. In general, of the the NACA0012 greater turbulence airfoil around outside 30%–60%c the boundary on the layer upper enhances surface flow forms stability, injects energy into the upstream laminar flow around the airfoil, and enhances the ability to a pressure platform. The Cf,X becomes negative at 18%c, which indicates that the flow is separated (Figuresresist adverse 13a and pressure 15a). The gradients, streamline so that around the lami NACA0012nar flow separation wraps a slendercould be eddy delayed due or to overcome. the laminar separationThen, the (Figurehigh-energy 15a). Thefluid SD7037 in the freestream airfoil also is experiences brought to flowthe near-wall separation, area but in the the separation flow mixing point process, which strengthens the stability of the turbulent shear layer to overcome the adverse pressure is slightly delayed, at about 25%c (Figure 17a). gradient, making it possible for the flow to reattach to the airfoil surface. When the angle of attack of the airfoils increases to 8 , flow separation occurs near the trailing In addition, compared with the NACA0012 airfoil, the◦ SD7037 airfoil has greatly delayed the edge of the NACA0012 airfoil at Tu = 6%, and a separation bubble forms near the trailing edge of the occurrence of transition and flow separation due to its good low-Reynolds-number performance, SD7037 airfoil (Figures 13b and 16b). At Tu = 0.6%, flow separation occurs near 4%c on the upper ensuring better adhesion of the boundary layer, and thus obtaining greater lift and stalling angle. surface of NACA0012 airfoil, and the separation area extends to the trailing edge (Figure 15b). Similarly, And the flow reattaches to form a trailing edge separation bubble on the upper surface of the SD7037 flowat Tu separation = 6%, which occurs is different near 14%c from on that the of upper the NACA0012. surface of SD7037 airfoil (Figure 17b). With the angle of attack increasing to 10◦, at Tu = 6%, a slender separation bubble is generated around 3%–16%c on4.2. the The upper Influence surface of Reyn of theolds NACA0012number on the airfoil, airfoil and the flow separation area near the trailing edge is expanded (Figure 14c). The location of trailing edge separation bubble on the SD7037 airfoil is The effect of Reynolds number on airfoils has been discussed a lot in the literature. The main slightly advanced, and a longer separation bubble is formed near 8%–20%c. At Tu = 0.6%, the pressure discussion here is on the airfoil aerodynamic performance with an increasing Reynolds number in distribution platform on the upper surface of the two airfoils appears earlier. The flow separation has terms of the improvement of stalling angle, generation of LSB, and the earlier transition. The pressure the characteristics of separation bubbles in terms of pressure distribution. distribution and chordwise friction drag coefficient of airfoils with an angle of attack of 10° in varied From the evolution of flow separation on the upper surface of the airfoils at Tu = 0.6% can be turbulence intensities at Re2 = 53,000 are shown in Figure 18. concluded that the increasing angle of attack results in the increase of adverse pressure gradient around the trailing edge, contributing to the separation of the boundary layer. Then the separation point
(a) (b)
Appl. Sci. 2020, 10, x FOR PEER REVIEW 14 of 20
(a) (b) (c)
Appl. Sci. 2020Figure, 10, 170617. The SD7037 airfoil characteristic such as turbulent kinetic energy and streamline shape at 14 of 19 Tu = 0.6%, (a) α = 5°; (b) α = 8°; (c) α = 10°. moves towardsFrom the the evolution leading of edge flow until separation the complete on the upper high-attack-angle surface of the separation,airfoils at Tu and= 0.6% stall can happens. be However,concluded the airfoil’s that the aerodynamic increasing angle performance of attack results improves in the and increase the process of adverse of separation pressure isgradient suppressed at Tuaround= 6%. the In general,trailing edge, the contributing greater turbulence to the separation outside of the the boundary boundary layerlayer. enhancesThen the separation flow stability, point moves towards the leading edge until the complete high-attack-angle separation, and stall injects energy into the upstream laminar flow around the airfoil, and enhances the ability to resist happens. However, the airfoil’s aerodynamic performance improves and the process of separation is adversesuppressed pressure at gradients,Tu = 6%. In so general, that the the laminar greater turbulence flow separation outside could the boundary be delayed layer or enhances overcome. flow Then, the high-energystability, injects fluid energy in the into freestream the upstream is broughtlaminar flow to the around near-wall the airfoil, area and in enhances the flow the mixing ability process, to whichresist strengthens adverse pressure the stability gradients, of the so turbulent that the lami shearnar layerflow separation to overcome could the be adverse delayed pressure or overcome. gradient, makingThen, it possiblethe high-energy for the flowfluid toin reattachthe freestream to the is airfoil brought surface. to the near-wall area in the flow mixing Inprocess, addition, which compared strengthens with the stability the NACA0012 of the turbulent airfoil, shear the layer SD7037 to overcome airfoil hasthe adverse greatly pressure delayed the occurrencegradient, of making transition it possible and flow for the separation flow to reattach due toto itsthe goodairfoil low-Reynolds-numbersurface. performance, ensuring betterIn addition, adhesion compared of the with boundary the NACA0012 layer, and airfoil, thus obtainingthe SD7037 greater airfoil lifthas andgreatly stalling delayed angle. the And the flowoccurrence reattaches of transition to form aand trailing flow edgeseparation separation due to bubbleits good on low-Reynolds-number the upper surface of performance, the SD7037 at Tu ensuring better adhesion of the boundary layer, and thus obtaining greater lift and stalling angle. = 6%, which is different from that of the NACA0012. And the flow reattaches to form a trailing edge separation bubble on the upper surface of the SD7037 4.2. Theat Tu Influence = 6%, which of Reynolds is different Number from onthat the of Airfoilthe NACA0012. The4.2. The eff ectInfluence of Reynolds of Reynolds number number onon the airfoils airfoil has been discussed a lot in the literature. The main discussionThe here effect is onof Reynolds the airfoil number aerodynamic on airfoils performance has been discussed with an a lot increasing in the literature. Reynolds The number main in termsdiscussion of the improvement here is on the of airfoil stalling aerodynamic angle, generation performance of LSB, with and an theincreasing earlier Reynolds transition. number The pressure in distributionterms of andthe improvement chordwise friction of stalling drag angle, coe generationfficient of of airfoils LSB, and with the an earlier angle transition. of attack The of 10pressure◦ in varied turbulencedistribution intensities and chordwise at Re2 = friction53,000 dr areag shown coefficient in Figure of airfoils 18. with an angle of attack of 10° in varied turbulence intensities at Re2 = 53,000 are shown in Figure 18.
(a) (b)
Figure 18. Airfoil aerodynamic performance at α = 10◦, Re2 = 53,000. (a) Pressure distribution; (b) Coefficient of chordwise friction drag.
It can be seen that flow separation, transition, and a short LSB occur around the leading edge of NACA0012 under both turbulence intensities at Tu = 0.6%, as well as SD7037. There is no appearance of separation or LSB on the upper surface of SD7037 at Tu = 6%, but Figure 18b shows that the transition still exists. In addition, combined with Figures 13c and 18, it can be seen that: With the increase of Reynolds number, the high-attack-angle separation around the trailing edge on the upper surface transfers to a small separation section, and the degree of flow separation is restrained. This shows that with the increase of Reynolds number, the shear effect on the airfoil surface is enhanced, the kinetic energy is more abundant, and the ability to resist the adverse pressure gradient is enhanced, so that the airfoil aerodynamic performance and stalling angle improves. Figure 19 shows the transformation of chordwise friction drag coefficient at angles of attack of 8◦ under three different Reynolds numbers. Taking the NACA0012 at Tu = 0.6% as an example, it can be seen that with the increase of Reynolds number, an earlier separation occurs on the upper surface of airfoil, the separation point transfers from 5%c to 2%c, and reattaches to the wall around 22%c, forming a typical structure of short LSB. When the Reynolds number increases to Re3 = 212,000, the position of the LSB transfers to 6%–13%c, and the Appl. Sci. 2020, 10, x FOR PEER REVIEW 15 of 20
Figure 18. Airfoil aerodynamic performance at α = 10°, Re2 = 53,000. (a) Pressure distribution; (b) Coefficient of chordwise friction drag.
It can be seen that flow separation, transition, and a short LSB occur around the leading edge of NACA0012 under both turbulence intensities at Tu = 0.6%, as well as SD7037. There is no appearance of separation or LSB on the upper surface of SD7037 at Tu = 6%, but Figure 18b shows that the transition still exists. In addition, combined with Figure 13c and Figure 18, it can be seen that: With
theAppl. increase Sci. 2020, 10of, xReynolds FOR PEER REVIEWnumber, the high-attack-angle separation around the trailing edge 15on of the 20 upper surface transfers to a small separation section, and the degree of flow separation is restrained.
This Figureshows 18.that Airfoil with aerodynamic the increase performance of Reynolds at αnu = mber,10°, Re the2 = 53,000shear. (effecta) Pressure on the distribution; airfoil surface (b) is enhanced,Coefficient the kinetic of chordwise energy friction is more drag. abundant, and the ability to resist the adverse pressure gradient is enhanced, so that the airfoil aerodynamic performance and stalling angle improves. FigureIt can be 19 seen shows that the flow transformation separation, transition, of chordwise and fra ictionshort LSBdrag occur coefficient around at the angles leading of attack edge of NACA0012 under both turbulence intensities at Tu = 0.6%, as well as SD7037. There is no appearance Appl.8° under Sci. 2020 three, 10, 1706 different Reynolds numbers. 15 of 19 of separation or LSB on the upper surface of SD7037 at Tu = 6%, but Figure 18b shows that the transition still exists. In addition, combined with Figure 13c and Figure 18, it can be seen that: With sizethe of increase the LSB of becomes Reynolds evidently number, smaller. the high-attack- In addition,angle the separation valley value around of C thef,X representstrailing edge the on onset the of laminarupper surface flow transition, transfers andto a peaksmall valueseparation after thesection, valley and of theCf,X degreerepresents of flow the separation finish of the is restrained. transition to turbulentThis shows flow. that Figure with 19the shows increase that of the Reynolds transition number, point the moves shear forward effect on from the 42%c airfoil through surface 17%c is toenhanced, 12%c, and the the kinetic reattachment energy is more point abundant, also moves and forward the ability from to resist 80%c the through adverse 25%c pressure to 13%c. gradient It can beis concludedenhanced, so that, that the the increasing airfoil aerodyna Reynoldsmic performance number results and st inalling earlier angle transition improves. and reattachment, contributingFigure to19 anshows overall the decreasetransformation in separation of chordwise bubble friction length, drag as stated coefficient in [38 at]. angles of attack of 8° under three different Reynolds numbers.
(a) (b) (c)
Figure 19. The chordwise friction drag coefficient of airfoil at α = 8° under the Reynolds number of (a) Re1 = 26,500; (b) Re2 = 53,000; (c) Re3 = 212,000.
Taking the NACA0012 at Tu = 0.6% as an example, it can be seen that with the increase of Reynolds number, an earlier separation occurs on the upper surface of airfoil, the separation point transfers from 5%c to 2%c, and reattaches to the wall around 22%c, forming a typical structure of short LSB. When the Reynolds number increases to Re3 = 212,000, the position of the LSB transfers to 6%–13%c, and the size of the LSB becomes evidently smaller. In addition, the valley value of Cf,X (a) (b) (c) represents the onset of laminar flow transition, and peak value after the valley of Cf,X represents the finish of the transition to turbulent flow. Figure 19 shows that the transition point moves forward FigureFigure 19. 19.The The chordwisechordwise friction drag drag coefficient coefficient of of airfoil airfoil at atα =α 8°= under8◦ under the Reynolds the Reynolds number number of (a) of fromRe 42%c1 = 26,500; through (b) Re17%c2 = 53,000 to 12%c,; (c) Reand3 = the212,000. reattachme nt point also moves forward from 80%c through (a) Re1 = 26,500; (b) Re2 = 53,000; (c) Re3 = 212,000. 25%c to 13%c. It can be concluded that, the increasing Reynolds number results in earlier transition andIn reattachment,Taking addition, the NACA0012 the contributing generation at toTu of an = the overall0.6% LSB as decrease aanffects example,the in separation aerodynamic it can be bubble seen characteristics thatlength, with as thestated of increase the in [38]. airfoils. of TheReynolds pressureIn addition, number, distribution the an generation earlier and separation chordwise of the LSB occurs friction affects on dragthe the aerodynamic coeupperfficient surface of characteristics airfoils of airfoi withl, the anof separation the angle airfoils. of attack point The of 5◦pressuretransfersin varied distributionfrom turbulence 5%c to and 2%c, intensities chordwise and reattaches at Re friction2 = 53,000 to drag the arewallcoefficient shown around inof 22%c, Figureairfoils forming 20with. an a angletypical of structureattack of 5°of inshort varied LSB. turbulence When the intensitiesReynolds numberat Re2 = 53,000increases are to shown Re3 = in212,000, Figure the 20. position of the LSB transfers to 6%–13%c, and the size of the LSB becomes evidently smaller. In addition, the valley value of Cf,X represents the onset of laminar flow transition, and peak value after the valley of Cf,X represents the finish of the transition to turbulent flow. Figure 19 shows that the transition point moves forward from 42%c through 17%c to 12%c, and the reattachment point also moves forward from 80%c through 25%c to 13%c. It can be concluded that, the increasing Reynolds number results in earlier transition and reattachment, contributing to an overall decrease in separation bubble length, as stated in [38]. In addition, the generation of the LSB affects the aerodynamic characteristics of the airfoils. The pressure distribution and chordwise friction drag coefficient of airfoils with an angle of attack of 5° in varied turbulence intensities at Re2 = 53,000 are shown in Figure 20.
(a) (b) (c)
Figure 20. Airfoil aerodynamic performance at α = 5◦, Re2 = 53,000. (a) Pressure distribution; (b) Coefficient of chordwise friction drag; (c)Effective shape of NACA0012 at Tu = 0.6%.
It can be seen that transition occurs on the upper surface of both airfoils and then laminar separation bubbles form at Tu = 0.6%. The generation of the laminar separation bubble changes the effective shape of the airfoil, increases the curvature of the upper surface of the airfoil (Figure 20c) so that the lift coefficient of the airfoil at Tu = 0.6% is bigger than that at Tu = 6%, and also causes the nonlinear phenomenon of the lift coefficient at small angle of attack as shown in Figures9a and 10a. (a) (b) (c) However, when the separation bubble size is small or forms near the trailing edge of the airfoil, it has little effect on the lift characteristics of the airfoil.
5. Discussion Through the comparison of the aerodynamic performance of different airfoils with different turbulence intensities and Reynolds numbers, it is found that the flow field around the airfoil is very unstable under low Reynolds number conditions, and the flow phenomenon on the suction side of the airfoil is abundant. The effects of turbulence intensity mainly appeared to be that with the increase of Appl. Sci. 2020, 10, 1706 16 of 19 turbulence intensity, the aerodynamic performance of airfoil becomes more stable, the lift improves, the stalling angle increases, and the occurrence of an LSB or flow separation can be suppressed to a certain extent. The numerical results show that under low Reynolds number conditions, the level of the turbulence intensity determines the flow characteristics (The external factors such as surface roughness and noise are not considered in this paper). In the fully developed turbulent boundary layer, most of the velocity fluctuation originate from the average shear flow, which is reflected in the production term of the turbulent kinetic energy equation. If the freestream turbulence is strong, the higher velocity fluctuations outside the boundary layer diffuse into the boundary layer near the airfoil surface. The intensity of this diffusion effect directly determines the occurrence of the transition. If the freestream turbulence is weak, the occurrence of transition is hardly affected by external disturbances, but basically caused by the instability of its inner flow so that external disturbances are only as a trigger. Mayle [39] pointed out that when the freestream turbulence intensity is higher than 3%, the effect of pressure gradient on the transition can be ignored. Transition is mainly affected by external disturbances. When the turbulence intensity is less than 1%, the pressure gradient and shear flow dominate the stability of flow. And the occurrence of transition at turbulence intensity of 1%–3% is affected by both external and inner factors such as freestream turbulence intensity and pressure gradient. The increase of the Reynolds number also causes the transition to move towards the leading edge, so that the lift and stalling angle increase, but the mechanism of the earlier transition is different from that of turbulence intensity. The increase of turbulence intensity leads to an earlier transition because of the higher velocity fluctuations that penetrate within the boundary layer. However, the increase of the Reynolds number alters the state of the boundary layer at separation reducing the shear layer thickness and consequently its stability characteristics. Simoni [28] also concluded that the Reynolds number significantly influences the time-mean boundary layer structure at separation. This translates into higher growth rates and different dynamic properties of the shedding phenomenon. In addition, the evolution of the LSB structure on the suction side of the airfoil is closely related to the Reynolds number. Taking the medium angle of attack (α = 8◦) of the NACA0012 airfoil at Tu = 0.6% as an example, at Re1 = 26,500, an eddy similar to a long laminar separation bubble emerges on the upper surface of the airfoil, but fails to reattach to the wall. At Re2 = 53,000, a small short laminar separation bubble is generated near the leading edge. At Re3 = 212,000, an LSB occurs on the upper surface of the airfoil near the trailing edge. These phenomena show that the generation of separation bubbles is closely related to the Reynolds number if the Reynolds number is too small, the laminar flow is not able to reattach to the wall after the transition, and it is difficult to form an LSB. As the Reynolds number increases, a complete LSB structure arises and the morphology of the LSB alters from a long separation bubble or a short separation bubble near the leading edge to a separation bubble near the trailing edge of the NACA0012 airfoil. It is worth noting that a separation bubble occurs at the trailing edge of the SD7037 airfoil at Re1 = 26,500, Tu = 6%, indicating that SD7037 has better low-Reynolds-number aerodynamic performance. This conclusion is consistent with the empirical criterion given by Carmichael [40]; Under natural laminar flow separation, the distance from flow separation to reattachment can be expressed as ReR Re = 50,000 (where Re is the Reynolds number of reattachment, Re is the Reynolds number of − S R S separation), which indicates that the separation flow of the airfoil will no longer reattach when the Reynolds number is less than 5 104,. Meanwhile, if the Reynolds number is slightly higher than × 5 104, a separation bubble will occur. Additionally, if the low-Reynolds-number performance of the × airfoil is excellent, the reattachment will also occur when the Reynolds number is less than 5 104. × 6. Conclusions In this paper, a numerical study was conducted on the influence of turbulence intensity and Reynolds number on the mean topology and transition characteristics of flow separation to provide better understanding of the unsteady jet flow of TeDP UAV. Through the comparative analysis of Appl. Sci. 2020, 10, 1706 17 of 19 the aerodynamic performance of the NACA0012 airfoil with experimental results, the numerical calculation method was verified. The effects of turbulence intensity and Reynolds number on aerodynamic performance of different airfoils, transition characteristics and evolution of LSBs were analyzed. The following conclusions are made. The increasing freestream turbulence intensity results in earlier transition and reattachment. At small angle of attack and higher turbulence intensity levels, airfoil encounters a minor decrease in lift, whereas at pre-stall angle of attack, lift increases and stall is delayed. Similarly, the increasing Reynolds number results in higher local vorticity Reynolds number and smaller flow energy dissipation, contributing to a stronger effect of the overall surface shear and earlier transition. The shear layer around airfoil can resist an adverse pressure gradient for a longer distance so that aerodynamic performance of the airfoil improves. However, the mechanism of earlier transition is different. The increase of turbulence intensity leads to an earlier transition because of the higher velocity fluctuations that penetrate within the boundary layer. However, the increase of the Reynolds number alters the state of the boundary layer at separation, reducing the shear layer thickness and consequently its stability characteristics. The generation of the LSB in laminar flow usually occurs at a Reynolds number of 50,000 and the evolution of the LSB structure on the suction side of the airfoil is closely related to Reynolds number and turbulence intensity. As the Reynolds number or turbulence intensity increases, the LSB will emerge earlier and its length will become shorter. The generation of the LSB changes the effective shape of the airfoil, and increases the curvature of the suction side of the airfoil, which causes the nonlinear phenomenon of the lift coefficient at small angle of attack. In addition, different airfoils have different sensibility to turbulence intensity and Reynolds number. Compared with the low-speed symmetrical airfoil, the low-Reynolds-number airfoil not only has superior performance in lift characteristics, but also in delaying flow separation. This research provides guidance for further airfoil design of the TeDP UAVs.
Author Contributions: Conceptualization, Y.Z. and Z.Z.; methodology, Y.Z. and X.L.; software, Y.Z.; validation, Y.Z., Z.Z. and K.W.; formal analysis, Y.Z.; investigation, Y.Z.; resources, Z.Z.; data curation, K.W., X.L.; writing—original draft preparation, Y.Z.; writing—review and editing, Y.Z.; supervision, K.W.; project administration, Z.Z.; funding acquisition, Z.Z. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by EQUIPMENT PRE-RESEARCH PROJECT, grant number 41411020401. Conflicts of Interest: The authors declare no conflict of interest.
Nomenclature
CD Coefficient of drag CL Coefficient of lift CP Coefficient of pressure CD,p Coefficient of pressure drag CD,f Coefficient of friction drag Cf,X Coefficient of friction in X direction Tu Turbulence intensity l Turbulence length scale RT Ratio of turbulence viscosity to laminar viscosity Tuinlet Turbulence intensity at the inlet of wind tunnel ε Turbulence dissipation rate k Turbulent kinetic energy γ Intermittence factor Rev Vorticity Reynolds number Sr Strouhal number d1 First layer grid element to wall distance TeDP Turboelectric distributed propulsion URANS Unsteady Reynolds-averaged Navier-Stokes Appl. Sci. 2020, 10, 1706 18 of 19
Refθt Transition momentum thickness Reynolds number LSB Laminar separation bubble FSTI Freestream turbulence intensity SST Shear stress transport
References
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