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Numerical Study of the Lift Enhancement Mechanism of Circulation Control in Transonic Flow
Numerical Study of the Lift Enhancement Mechanism of Circulation Control in Transonic Flow
Chen, Ye;Hou, Zhongxi;Deng, Xiaolong;Guo, Zheng;Shao, Shuai;Xu, Boting
aerospace Article Numerical Study of the Lift Enhancement Mechanism of Circulation Control in Transonic Flow 1 1 1 1, 1 2 Ye Chen , Zhongxi Hou , Xiaolong Deng , Zheng Guo *, Shuai Shao and Boting Xu College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China; email@example.com (Y.C.); firstname.lastname@example.org (Z.H.); email@example.com (X.D.); firstname.lastname@example.org (S.S.) Center of Strategic Assessments and Consulting, Academy of Military Sciences, Beijing 100091, China; email@example.com * Correspondence: firstname.lastname@example.org Abstract: The lift of an aircraft can be effectively enhanced by circulation control (CC) technology at subsonic speeds, but the efﬁciency at transonic speeds is greatly decreased. The underlying mechanism of this phenomenon is not fully understood. In this study, Reynolds averaged Navier— Stokes simulation with k w shear stress transport model was utilized to investigate the mechanism of lift enhancement by CC in transonic ﬂow. For validation, the numerical CC results were compared with the NASA experimental data obtained for transonic CC airfoil. Thereafter, the RAE2822 airfoil was modiﬁed with a Coanda surface. The lift enhancement effects of CC via steady blowing with different momentum coefﬁcients were tested at Ma = 0.3 and 0.8 at a = 3 , and various ﬂuid mechanics phenomena were investigated. The results indicate that the ﬂow structure of the CC jet is insensitive to the incoming ﬂow conditions because of the similarity to the local static pressure ﬁeld around the trailing edge of the airfoil. Owing to the appearance of shockwaves on the airfoil surface in the transonic regime, the performance of the CC jet is restricted to the trailing edge of Citation: Chen, Y.; Hou, Z.; Deng, X.; the airfoil. Transonic CC achieved a slight improvement in aerodynamic performance owing to a Guo, Z.; Shao, S.; Xu, B. Numerical favorable shift in the shockwave pattern and accelerated ﬂow in the separation region on the airfoil Study of the Lift Enhancement surfaces. Revealing the mechanism of lift enhancement of CC in the transonic regime can facilitate Mechanism of Circulation Control in Transonic Flow. Aerospace 2021, 8, 311. the rational design of new ﬂuidic actuators with high activity and expand the potential applications https://doi.org/10.3390/ of CC technology. aerospace8110311 Keywords: circulation control; effectiveness; transonic ﬂow; ﬂow control Academic Editor: Pietro Catalano Received: 22 September 2021 Accepted: 15 October 2021 1. Introduction Published: 20 October 2021 Circulation control (CC) is a widely known method of augmenting the lift on a wing [1,2]. CC, as a high-lift device, was ﬁrst studied in the late 1930s . Later, a CC Publisher’s Note: MDPI stays neutral airfoil concept based on the Coanda effect was patented by Davidson in 1962 . Generally, with regard to jurisdictional claims in the airfoil is equipped with span-wise dual blowing slots that emit a high-momentum jet published maps and institutional afﬁl- tangentially along a curved trailing edge [5–7]. Control of airfoil circulation (lift), both iations. positive and negative, can be achieved by individually controlling the blowing from the upper and lower slots on the trailing edge, similar to the control surfaces of conventional aircrafts (e.g., ailerons or ﬂaps) . Previously, Englar  and Englar and Huson  suggested that a CC wing (CCW) Copyright: © 2021 by the authors. could signiﬁcantly enhance the lift. Recently, CC has been studied as an alternative Licensee MDPI, Basel, Switzerland. control method for ﬂapless aircrafts [11,12]. This new technology can decrease the sig- This article is an open access article nature by reducing the traditional moving control surfaces, which makes it essential in distributed under the terms and ﬂight control [13,14]. For example, the ICE and SACCON unmanned aerial vehicles of conditions of the Creative Commons NATO task group AVT-239 were built and ﬂown to demonstrate the effectiveness of this Attribution (CC BY) license (https:// concept [15,16]. creativecommons.org/licenses/by/ 4.0/). Aerospace 2021, 8, 311. https://doi.org/10.3390/aerospace8110311 https://www.mdpi.com/journal/aerospace Aerospace 2021, 8, 311 2 of 19 Experimental [5,17,18] and numerical investigations [3,19,20] have been conducted in a wide range of studies on the CC mechanism to improve the effectiveness of CC. Wood and Nielsen  and Novak and Cornelius  indicated that the efﬁciency of a CC system could be improved by increasing the velocity of the tangentially blown jet. When a high-velocity CC jet passes over the Coanda surface, it can entrain lower-momentum ﬂuid from local external ﬂow near the trailing edge of the airfoil, delaying separation, shifting the stagnation points, increasing the circulation, and augmenting the lift. However, the effectiveness of CC does not increase unlimitedly with increasing momentum coefﬁcient C . According to Li and Qin  and Cornelius and Lucius , the increment in lift will decrease as C increases to a certain extent due to CC jet detachment, which is called “C -stall”. CC jet detachment mainly results from an adverse pressure gradient as it moves along the trailing edge circumference. In addition, previous scholars [24,25] have found that the effectiveness of CC could be strongly inﬂuenced by the incoming ﬂow. These researchers demonstrated that CC can enhance the lift at transonic speeds, but it is less effective than at subsonic speeds. There- fore, less attention has been paid to CC in the transonic regime. In the 1980s, researchers mainly focused on the CC of helicopter rotor blade applications at transonic speeds [25–27]. Recently, researchers have focused on parametric evaluation  and optimization  of the CC airfoil to improve the transonic performance. Forster et al.  demonstrated the feasibility of RANS with the k w SST turbulence model for the simulation of CC in the transonic regime. Milholen et al.  highlighted the drawbacks of transonic CC when researching the fundamental aerodynamics subsonic/transonic-modular active control (FAST-MAC). The experiments on FAST-MAC conducted in their study were considered unique, as they evaluated CC strategies at transonic speeds. However, the physical mecha- nism of CC at transonic freestream speeds has rarely been discussed. The aim of this study was to compare the behaviors of CC in transonic ﬂow to those in subsonic ﬂow to improve understanding of the mechanism of lift enhancement by CC in high-speed ﬂows. The effect of free incoming ﬂow on the effectiveness of CC was studied in detail via a numerical method. Rather than optimizing the geometries and conﬁgurations of Coanda devices intuitively to improve the transonic performance, careful attention was paid to identifying the cause of the reduced effectiveness of CC in transonic ﬂow. Our ﬁndings provide novel insights into the role of the CC system in transonic freeﬂow. A favorable shift in the shockwave pattern and accelerated ﬂow in the separation region on the airfoil surface by CC resulted in lift enhancement in transonic ﬂow. These ﬁndings may provide a new direction for research into CC technology. However, CC for lift enhancement purposes could not be made to operate on conﬁgurations ﬂying at practical (at least transonic) ﬂight speeds. Understanding the inferior performance of CC operating in transonic incoming ﬂow will facilitate the rational design of CC systems for practical applications, although further studies remain necessary. To achieve the aim of this study, two types of RAE2822 airfoil with CC under the freestream conditions of Ma = 0.3 and 0.8 at a = 3 were examined for comparison of the ﬂow phenomenon. The remainder of this paper is organized as follows. Firstly, the numerical methods are elucidated in Section 2 and validated by comparison to CCW experimental data in Section 3. In Section 4, the change in the behavior of the CC jet from subsonic to transonic speeds is examined, including the pressure coefﬁcient distribution on the Coanda surface, wave structure, and entrainment characteristics of the CC jet. Thereafter, the interactions of the CC jet with external ﬂow around the RAE2822 airfoil are analyzed to provide further insight into the mechanism of lift enhancement by CC in transonic ﬂow in Section 5. 2. Numerical Methods The numerical approach utilized in this study is based on the ﬁnite-volume method, in which the computational ﬂuid dynamics (CFD) code provides complete mesh ﬂexibility. The steady and compressible Reynolds averaged Navier–Stokes (RANS) equations were Aerospace 2021, 8, 311 3 of 19 used to predict CC under subsonic and transonic conditions. The gravitational and external body forces were ignored. For spatial discretization, the second-order upwind scheme was utilized to determine the convection, pressure, and viscous terms. The ﬂux type was discretized by Roe-averaged ﬂux difference splitting. The second-order upwind scheme with the min–mod limiter was used to determine the state-variable interpolations on the cell faces. Time integration was performed by using the lower-upper symmetric Gauss–Seidel (LU-SGS) schemes. The working ﬂuid was set to the ideal gas. The viscosity coefﬁcient m was calculated by Sutherland’s law. The k w SST turbulence model was that used in . 3. Validation of Trailing-Edge CC The aerodynamic performance of the CCW obtained by using the numerical method was validated by comparison with the experimental data obtained by Alexander et al. in 2005 . The elliptical airfoil of the wing is shown in Figure 1. The camber of the airfoil was 0.75% chord, and the thickness was 6% chord. The trailing edge of the airfoil was modiﬁed as a 2.98:1 elliptical Coanda surface with a slot height to chord ratio of 0.12%. The experimental model conﬁguration is shown in Figure 2a. The span of the wing model is two chord lengths, with an end plate of one chord length in diameter to minimize the ﬁnite span effect. The diameter of the end plate was enlarged to 1.1 chord lengths in this study to enable the structured blocks to wrap around the leading edge of the airfoil. The geometric model difference can be ignored, as conﬁrmed by the CFD validation study of Forster and Steijl . A circular splitter plate with a diameter of six chord lengths was included in the conﬁguration to ensure more accurate solutions, because similar studies [26,32] of the CCW conﬁguration suggested that modeling of the viscous wall of the splitter plate was necessary for more accurate solutions. Figure 1. Elliptical airfoil with Coanda surface. A grid reﬁnement study was performed based on the results obtained by Li and Qin  and Forster et al. . The baseline grid setting involved 221 cells on the airfoil, as shown in Figure 2b, 121 cells on the Coanda surface, 149 cells in the wall-normal direction, and 221 cells over the span of the airfoil . Accordingly, the medium grid and ﬁne grid were, respectively, 1.5 and 2 times the number of baseline grids. The numbers of ﬁne 6 6 grids for the models without and with blowing were approximately 23 10 and 24 10 , respectively. The distance of the ﬁrst grid point near the wall in all computational cases was held constant to maintain y O(1). The computational domain was surrounded by four types of boundary conditions: viscous walls, pressure far ﬁeld, symmetry, and pressure inlet conditions, as shown in Figure 3. The cylindrical pressure far-ﬁeld surface was located 10 chord lengths away from the center of the airfoil in the radial direction and 7 chord lengths from the splitter plate in the span-wise direction. The subsonic freestream ﬂow conditions were set to Ma = 0.3, a = 3 , and Re = 1.0 10 , and the transonic freestream ﬂow conditions were set to Ma = 0.8, a = 3 , and Re = 2.0 10 . The Reynolds number based on the freestream ﬂow velocity U and chord lengths c of the modiﬁed airfoil was expressed as Re = rU c/m. ¥ ¥ Aerospace 2021, 8, 311 4 of 19 Figure 2. Experimental model conﬁguration of CCW and structured grid around the splitter plate. Figure 3. Computational domain of CCW. The experimental and computational results for the surface pressure coefﬁcients of the midspan wing section at Ma = 0.3 without blowing are compared in Figure 4. The three grid sets for the 3D model agree well with the experimental data. In addition, the medium and ﬁne meshes coincide well with each other. Although the computational results for the leading edge of the coarse mesh are slightly higher than those for the other two mesh resolutions, the differences in the mesh inﬂuence could be neglected. Because the current numerical and coarse grid settings could effectively simulate the ﬂow around the CCW model, the coarse grid scheme was selected for subsequent analysis and comparison, resulting in only a slight decrease in computational accuracy. The computational results of the 2D airfoil are also shown in Figure 4. The value of static pressure coefﬁcient C of the 2D airfoil shows large discrepancies from the experimental data, indicating that the tunnel wall boundary conditions signiﬁcantly affect the leading-edge surface pressure distribution. The 3D effects of the wing model are also reported along with the computational  and experimental results . Aerospace 2021, 8, 311 5 of 19 Figure 4. Comparison of C on the midspan wing section of the unblown case (Ma = 0.3, a = 3 ). Computational domain of CCW. The experimental  and computational results for C on the midspan wing section in the case of upper slot blowing are compared in Figure 5. For Ma = 0.3 (Figure 5a), there is satisfactory agreement between the measured and CFD results. The cases without blowing and with momentum coefﬁcient C 0.029 agree well with the experimental results. There are subtle differences between the CFD and experimental results on the Coanda surface at high C 0.054, but the results correctly capture the peak pressure at the leading edge of the airfoil. The differences may have resulted from the complex ﬂuid phenomena (e.g., SBLI ) occurring on the Coanda surface at high C , which cannot be captured well by the coarse grid. C is deﬁned as Equation (1): m ˙ U jet C = , (1) q A where m ˙ is the mass ﬂow rate through the slot exit; A is the wing surface area;q is the freestream dynamic pressure. Based on the assumption  that the jet ﬂow expands out of the slot isentropically to reach the freestream static pressure p , we can obtain the jet velocity U from Equation (2): jet 2 3 g 1 u 2g p t 4 5 U = RT 1 , (2) jet 0 g 1 p 0, plenum where p is the total plenum pressure and T is the total temperature at the pressure 0, plenum 0 inlet; g is the speciﬁc heats ratio. For Ma = 0.8, the pressure coefﬁcients in the cases of no blowing and upper slot blowing for C 0.008 and C 0.014 were compared with the experimental data, as m m shown in Figure 5b. The results indicate a systematic error between the CFD and the experimental results. The pressure coefﬁcients on the leading edge of the upper airfoil surface are over-predicted by the present numerical methods for the cases with and without blowing. This systemic error was also observed by Foster and Steijl  and Li and Qin  while studying the numerical pressure coefﬁcients of transonic CC. No clear cause of the systemic error was determined, but the present numerical method is considered to capture the pressure coefﬁcients with the relevant ﬂow physics. It is believed that the present numerical method can provide the pressure coefﬁcients with reasonable accuracy. Aerospace 2021, 8, 311 6 of 19 Figure 5. Comparisons of pressure coefﬁcients under upper slot blowing (Ma = 0.3 and 0.8 at a = 3 ). The results for the case without slot blowing are also depicted. Figure 6 compares the changes in the lift coefﬁcient with increasing momentum coefﬁcient between the experimental data and the present CFD results. For both Mach numbers, the trend of lift augmentation with increasing C is captured by the numerical method, which indicates that the numerical results can reveal the ﬂow physics of CC in the subsonic and transonic regimes. However, in the high C range, the CFD approach over-predicted the lift augmentation in the transonic regime, but underestimated the value in the subsonic regime. Similar results were presented in [1,29], and the precise reasons were complex and inconclusive. In general, the comparisons show satisfactory agreement between the experimental data and CFD results for the aerodynamic performance of CCW in the subsonic and transonic regimes over a wide range of Coanda jet blowing, which indicates that the method can achieve acceptable numerical accuracy. Figure 6. Comparisons of changes in the lift coefﬁcient (DC = C C ) due to variation in L L L C 6=0 C =0 m m C with upper slot blowing for Ma = 0.3 and 0.8 at a = 3 . 4. Flow Physics of CC Jet in Transonic and Subsonic Incoming Flows 4.1. Numerical Model Setup of the RAE2822 Airfoil with CC The RAE2822 airfoil was used here to investigate the mechanism of the reduced CC capability at transonic speed. The airfoil was truncated at x/c = 0.943 to include a orig trailing-edge Coanda surface. c denotes the chord length of the airfoil before truncation. orig Figure 7 shows the trailing edge of the modiﬁed airfoil. In this study, the parameters of Aerospace 2021, 8, 311 7 of 19 the Coanda surface were chosen based on the geometry of the trailing edge illustrated in Section 3. The elliptical trailing edge with a length r to height r ratio of 2.98:1 was added TE s to the airfoil, q is the Coanda surface termination angle and a slot height to chord ratio of 0.05% was selected (as illustrated in Figure 8). Figure 7. RAE2822 airfoil with Coanda surface. Figure 8. Trailing edge of the RAE2822 airfoil. The boundary conditions are the same as in the CCW case in Section 3. The total pressure of the plenum inlet ﬂow p was determined based on the static pressure of 0,plenum the freestream p and the nozzle pressure ratio (NPR): p = p NPR. The total ¥ 0,plenum ¥ temperature T of the nozzle inlet ﬂow was 300 K. In this study, the NPR was ﬁxed, and the C was calculated a posteriori by integrating the solution along the slot exit. The NPR and corresponding C values are listed in Table 1. The freestream speeds were obtained at 6 6 Ma = 0.3, a = 3 , Re = 1.0 10 and Ma = 0.8, a = 3 , Re = 2.0 10 . The freestream c c temperature T was 300 K. The turbulence intensity of the freestream was set to 5%, and the turbulent viscosity ratio was 10. The no-slip wall boundary condition was applied to the airfoil surface, Coanda surface, and plenum surfaces. Table 1. Correspondence between NPR and C . NPR Ma = 0.3 Ma = 0.8 1.1 0.0015 0.0002 2 0.0130 0.0018 4 0.0359 0.0050 6 0.0598 0.0084 8 0.0846 0.0119 10 0.1100 0.0154 12 0.1357 0.0191 14 0.1619 0.0228 16 0.1882 0.0265 Aerospace 2021, 8, 311 8 of 19 Grid independence analysis was conducted based on the node distributions of the wing with elliptic airfoil in Section 3; the number of grid points was 7.3 10 (coarse), 4 4 10.9 10 (medium), and 14.6 10 (ﬁne). During the reﬁnement, the distance of the ﬁrst grid point from a solid wall was held constant to maintain y O(1). The computational mesh is shown in Figure 9. The pressure distributions on the airfoil surface for the different grids at Ma = 0.3 and Ma = 0.8 with the blowing momentum coefﬁcients of 0.0015 and 0.0002, respectively, are presented in Figure 10. The results demonstrate that the grid has little inﬂuence on the cases of subsonic ﬂow and transonic ﬂow. Because the interaction of the CC jet with the external ﬂow near the trailing edge is very complex, the ﬁne grid scheme was selected for the subsequent analysis to capture the ﬂow characteristics. Figure 9. Medium mesh around the trailing edge for RAE2822 with Coanda surface (Ma = 0.3 at a = 3 ). Figure 10. Inﬂuence of grid resolution for Ma = 0.3 and 0.8 at a = 3 . We examined the load control effects of CC for the RAE2822 airfoil under the freestream conditions of Ma = 0.3 and 0.8 at a = 3 . The lift coefﬁcient augmentation under a range of blowing momentum coefﬁcients is shown in Figure 11. The maximum augmentation in the lift coefﬁcient reaches 0.89 at Ma = 0.3, whereas this value is only 0.21 when the freestream conditions are Ma = 0.8. The load control capability of CC at transonic speeds is much lower than that at subsonic speeds, which was also observed by Alexander et al. . Aerospace 2021, 8, 311 9 of 19 Figure 11. Lift coefficient augmentation for a range of momentum coefficients under steady conditions. Furthermore, the effectiveness of CC is limited under both incoming ﬂow conditions. The augmentation of the lift coefﬁcient increases to the maximum value and starts to oscil- late, then decreases dramatically, which indicates the occurrence of “C -stall”. Figure 11 also shows the standard deviation in the case of oscillations. The “C -stall” point occurs at approximately C = 0.1619 and 0.0228 for Ma = 0.3 and 0.8, respectively. In summary, the load control capability of CC is limited under both sets of incoming ﬂow conditions, and the effectiveness of CC at transonic speeds is very low when compared with that at subsonic speeds. 4.2. CC Jet Behaviors at Ma = 0.3 and 0.8 The reduced CC capacity under transonic speeds may be attributed to the effect of the local external ﬂow on the CC jet behavior. A previous report  noted that the external ﬂow adjacent to the shear layer of the CC jet reduced the local static pressure p, effectively increasing the nozzle pressure ratio and promoting the expansion of the CC jet, and ultimately altering the CC jet ﬂow behavior. To quantify the effect of the local external ﬂow on the CC jet behavior, we deﬁne the effective nozzle pressure ratio as NPRe = p /p, which is the ratio of the total pressure in the plenum to the local 0,plenum static pressure. Because NPRe = p /p p /p = NPR p /p, the ampliﬁcation ¥ ¥ ¥ 0,plunem coefﬁcient # was used as a measure of the effect of the local external ﬂow on the CC jet expansion, which is deﬁned as Equation (3): # = . (3) Here, the ampliﬁcation effect of the external ﬂow at the trailing edge is discussed and compared for the two cases of incoming ﬂow. The freestream condition is Ma = 0.3 and Ma = 0.8 at a = 3 . The # contours of the baseline case are presented in Figure 12. The # range is 0.92–0.98 for Ma = 0.3 and 0.96–0.98 for Ma = 0.8. The pressure recovers to a value slightly above at the trailing edge for both Mach numbers owing to skin friction drag and ﬂow separation. There is only a slight difference in the ampliﬁcation effect between these two incoming ﬂows. Consequently, the effect of the local external ﬂow on the CC jet behavior is almost negligible. Aerospace 2021, 8, 311 10 of 19 Figure 12. Ampliﬁcation coefﬁcient contours of the baseline model. A similar variation in C along the upper Coanda wall reﬂects the characteristics of pt the under-expanded CC jet in both freestreams, which further supports the above con- clusion. The surface pressure coefﬁcient C is deﬁned as C = (p p )/p . pt pt s 0,plenum 0,plenum The variable p denotes the surface static pressure distribution. Figure 13 shows the C s pt distributions on the Coanda surface for Ma = 0.3 and Ma = 0.8. For the same NPR values, only a slight discrepancy in the distribution is found between Ma = 0.3 and Ma = 0.8, which indicates that the CC jet features are very similar for both incoming ﬂows for the same NPR. Figure 13. Pressure coefﬁcient C on the Coanda surface for Ma = 0.3 and 0.8 at various NPRs. pt However, the NPRs signiﬁcantly inﬂuence the C distribution in both incoming ﬂows, pt which is reﬂected in the changes in the CC jet behavior. The Ma contours around the upper trailing-edge surface are shown in Figure 14 to visualize the CC jet behavior. At a moderate blowing pressure with NPR = 2 (Figure 14a), the wave structure is smooth and regular, implying a fully attached boundary layer all along the Coanda surface. Remarkable growth in the oscillation magnitude can be observed at NPR = 6 (Figure 14b). The strong adverse pressure gradient regions in the ﬁrst two troughs indicate separation. After each separation, there are favorable pressure gradient regions, indicating reattachment. At the critical NPR = 14 (Figure 14c), the ﬁrst two separated troughs merge, and a small trough follows and extends to the end of the Coanda surface, which indicates that the attachment has become weak. Finally, at NPR = 16 (Figure 14d), the jet ﬂow is vectored from the surface, as the extension of the region of local separation beyond the edge of the Coanda surface allows air at atmospheric pressure to be drawn into the separation bubble. Hence, the boundary-layer control of the CC jet fails. Aerospace 2021, 8, 311 11 of 19 Figure 14. Mach number contours for Ma = 0.3 (left column) and Ma = 0.8 (right column) with a = 3 to characterize the jet behavior of a supersonic CC jet with increasing NPR (a) upon attachment to the reaction surface, (b) upon the formation of separation bubbles, (c) just before separation, and (d) upon full separation. 4.3. Flow Field Structure at NPRs of 14 and 16 4.3.1. Shock Structures The numerical schlieren (density gradient), which provides an ideal initial inspection of the wave structure along the Coanda surface, was used to obtain the results for both freestream Mach numbers, as presented in Figure 15. The density gradient is deﬁned as, ds = c1 exp(( c2 (j5rj j5rj )/(j5rj j5rj )), where c1 and c2 are constants, min max min as in the studies by Wu and Martin  and Tong et al. . The ﬂow ﬁelds for all cases show large expansion fans at the nozzle exit. At NPR = 14, the SBLI generated by the Coanda surface are presented downstream from the expansion fan in the ﬂow ﬁeld, as shown in Figure 15a,b. Furthermore, the reﬂected shockwave appears at the onset of the separation bubble owing to the adverse pressure gradient. At NPR = 16, the ﬂow expansion is terminated by the oblique shock downstream, as shown in Figure 15c,d. The Aerospace 2021, 8, 311 12 of 19 shock structures of the CC jet in the transonic incoming ﬂow are similar to those of the subsonic incoming ﬂow under the same NPR conditions. Figure 15. Density gradient ﬁelds of the jet along the Coanda surface. 4.3.2. Shear Layer Development The entrainment characteristics around the CC jet near the trailing edge can be accu- rately represented and examined through ﬂow quantities, such as the turbulent kinetic 0 0 0 0 energy (TKE), k = 0.5(u u + u u ) . Fortunately, the TKE is evaluated during the x x z z solution process when the SST RANS model is used and is explicitly available as an output variable. Figure 16 reveals the inﬂuence of In addition, the details of the TKE for NPR = 14 at ﬁve speciﬁc stations are illustrated in Figure 17. The results suggest that the cases corresponding to Ma = 0.8 possess slightly better entrainment characteristics than those corresponding to Ma = 0.3. Based on the above analysis, various ﬂuid mechanic phenomena are presented, in- cluding shock waves, expansion fans, boundary layers, shock/boundary-layer interactions, ﬂow separation, and entrainment. The ﬂow behavior of the CC jet at Ma = 0.8 shows a high degree of similarity with that at Ma = 0.3. The entrainment characteristics at Ma = 0.8 is better than that at Ma = 0.3. The results indicate that the load control capability of CC at transonic speeds should be comparable or even superior to that at subsonic speeds; however, the effectiveness of the CC jet remarkably decreases at transonic speeds, for reasons that will be detailed later. Aerospace 2021, 8, 311 13 of 19 Figure 16. Growth of the jet shear layers based on k 10,000. Figure 17. Turbulent kinetic energy at speciﬁc locations for NPR = 14. 5. Mechanisms of Lift Augmentation in Transonic Flow 5.1. Mechanism of Lift Augmentation for Subsonic Freestream The mechanism of lift augmentation for the CC jet in subsonic ﬂow is discussed in this section. The global view of the effects of CC on the mean ﬂow streamlines for Ma = 0.3 is presented in Figure 18. The mean ﬂow streamlines around the leading and trailing edges of the baseline model are almost parallel to the freestream (a = 3 ) (Figure 18a). Owing to blowing at NPR = 14 over the upper Coanda surface, the streamlines at the trailing edge of the airfoil are signiﬁcantly entrained downward by the CC jet. Moreover, the streamlines at the leading edge of the airfoil are deﬂected downward, increasing the angle of attack. The mean streamlines are concave-down due to the CC jet (Figure 18b). In contrast, when the CC jet at NPR = 16 detaches from the upper Coanda surface, the mean streamline is concave-up (see Figure 18c). The CC jet at NPR = 14 increases the ﬂow velocity near the upper surface, but decreases it near the lower surface. Consequently, the pressure coefﬁcients along the entire surface of the airfoil are changed owing to differences in the ﬂow velocity near the airfoil surface, especially in the leading-edge region, as shown in Figure 19. The detached CC jet at NPR = 16 has the opposite effects on the velocity ﬁeld around the airfoil, resulting in reduced lift. Aerospace 2021, 8, 311 14 of 19 Figure 18. Effects of the CC jet on streamline shapes with increasing NPR for Ma = 0.3, a = 3 . Figure 19. Comparison of pressure coefﬁcients due to changes in NPR (Ma = 0.3). The entrainment characteristics forMa = 0.3 around the airfoil are illustrated in Figure 20. The locations of increased TKE are consistent with the deﬂected mean ﬂow streamlines resulting from the CC jet. These results indicate that the acceleration of the ﬂow ﬁeld around the airfoil is associated with the momentum injection effects of the CC jet. Aerospace 2021, 8, 311 15 of 19 Figure 20. Entrainment characteristics with increasing NPR (Ma = 0.3). 5.2. Mechanism of Lift Augmentation for Transonic Freestream Unlike in the case with Ma = 0.3, curving streamlines caused by the CC jet are not found in the transonic incoming ﬂow, as shown in Figure 21. However, the CC jet causes a shift in the supersonic region around the airfoil. Shockwave pattern variation was also observed by Milholen et al. . The C distribution on the airfoil with Ma = 0.8 at a = 3 is illustrated in Figure 22 to analyze the effect of the CC jet on the ﬂow ﬁeld. With increasing NPR, a signiﬁcant increase in the pressure difference between the upper and lower airfoil surfaces occurs around the rear region of the airfoil. However, the pressure coefﬁcient before the terminating shock wave remains almost unchanged. Figure 21. Effects of the CC jet on the streamline shapes with increasing NPR for Ma = 0.8 at a = 3 . Moreover, the CC jet affects the positions of both upper and lower shocks on the airfoil. The upper shock wave moves from 0.564c to 0.588c, resulting in the extension of the supersonic region of the upper surface and enhanced strength of the upper shock wave. The position of the lower shock wave moves forward from 0.540c to 0.499c, resulting in the Aerospace 2021, 8, 311 16 of 19 recession of the supersonic zone of the lower surface. In addition, the strength of the lower shock wave is decreased. The CC jet in the transonic incoming ﬂow can accelerate the ﬂow around the trailing edge of the airfoil and modify the shock around the airfoil, which is the main lift enhancement mechanism of CC in transonic ﬂow. Figure 22. Comparison of pressure coefﬁcients due to changes in NPR (Ma = 0.8). The mode of action of the CC jet in the transonic regime differs from that in the subsonic regime. These differences are attributable to the presence of shock on the upper surface of the airfoil. When the ﬂow becomes supersonic near the airfoil surface, the disturbances in the CC jet cannot advance upstream from the terminating shock wave. Hence, the CC actuation on the airfoil no longer affects the external ﬂow at the leading edge and cannot continue to entrain the ﬂow to follow the CC jet; consequently, the pressure coefﬁcient on the leading edge of the airfoil is unaffected. In the subsonic regime, the pressure change spreads over the rest of the airfoil more evenly, signiﬁcantly increasing the effectiveness of the CC device. The CC jet in the incoming transonic ﬂow affects the ﬂow in its vicinity, which leads to a signiﬁcant pressure decrease around the trailing edge. The low-pressure region of the trailing edge is mainly attributed to the local acceleration by the downstream CC jet. The mean turbulence quantities provide further insight into the ﬂow ﬁeld. The entrainment characteristics at Ma = 0.8 around the airfoil are illustrated in Figure 23. A high-level TKE at the rear region of the baseline airfoil, resulting from severe ﬂow separation downstream of the shocks, is presented in Figure 23a. At NPR = 14, an increase in the TKE is observed in the separation region, which coincides well with pressure decrease at the trailing edge (Figure 23b). The results indicate that additional momentum offered by the CC jet re- energizes and accelerates the ﬂow in the separation region, which eventually induces an increase in the lift coefﬁcient. This result is consistent with the ﬁndings by Itsariyapinyo and Sharma  and Milholen et al. . At NPR = 16, the TKE values in the separation region are decreased when compared with the baseline (Figure 23c). These decreases may result from the ﬂow velocity inhibition effects of the detached CC jet, which explains the aerodynamic performance degradation. Aerospace 2021, 8, 311 17 of 19 Figure 23. Entrainment characteristics with increase in NPR (Ma = 0.8). 6. Conclusions The effectiveness of CC in the transonic regime is less than that in the subsonic regime. To identify the reason for this phenomenon, the lift enhancement mechanisms related to CC in transonic ﬂow were numerically investigated. Firstly, the CFD results were compared against the experimental data to validate the CC. The RAE2822 airfoil with the modiﬁed trailing edge was selected for the investigation of freestreams with Ma = 0.3 and 0.8 at a = 3 . The ﬂow ﬁelds generated by a series of CC jets at the trailing edge of the airfoil were compared, and the results were analyzed. The following conclusions can be drawn. The pressure coefﬁcient on the Coanda surface and ﬂow-ﬁeld structures of the CC jet in transonic ﬂow, including the shock structures and entrainment characteristics, are very similar to those observed in subsonic ﬂow, emphasizing the insensitivity of the CC jet to the freestream Mach number. The insensitivity is mainly due to the similarity in the static pressure ﬁeld of the trailing edge of the RAE2822 airfoil. A shockwave on the upper surface of the airfoil is the main reason for the decreased lift enhancement by CC in the transonic regime. In this regime, the CC jet disturbances cannot propagate upstream from the shockwave, limiting its performance to the trailing edge of the airfoil. In contrast, the disturbances created by the CC jet in the subsonic regime spread more evenly throughout the airfoil. Nevertheless, the CC jet can still enhance the lift in the transonic regime by positively altering the shockwave pattern on the airfoil surfaces and accelerating the ﬂow in the separation region by promoting momentum transfer. The lift enhancement mechanism of CC in the transonic regime was elucidated, facilitating the expansion of the utilization of this technology. Reducing the transonic drag on the aircraft may constitute a new direction for research. Furthermore, by understanding the mechanism of lift enhancement of CC in transonic regime, new ﬂuidic actuators with high activity can be rationally designed, although it seems unlikely that CC will perform better as a high-lift technique in a transonic regime due to the different lift enhancement mechanisms. However, our subject was just a representative supercritical airfoil, and further studies remain necessary. Author Contributions: Conceptualization, Y.C., Z.H., and Z.G.; methodology, Y.C.; validation, Y.C. and S.S.; writing—original draft preparation, Y.C., X.D., Z.G., and B.X.; writing—review and editing, Y.C. and B.X.; visualization, Y.C.; supervision, X.D. and Z.G.; funding acquisition, X.D. All authors have read and agreed to the published version of the manuscript. Aerospace 2021, 8, 311 18 of 19 Funding: This research was funded by the National Natural Science Foundation of China, grant number 52172410 and 61903369. 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Numerical Study of the Lift Enhancement Mechanism of Circulation Control in Transonic Flow
, Volume 8 (11) –
Oct 20, 2021
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