Int'l Cnference n Research & Innvatin in Cmputer, Electrnics and Manufacturing Engineering (RICEME-7) Feb. 2-3, 27 Bali (Indnesia) A Study f Aerdynamic Characteristics f an Anti-tank Missile Chun-Chi Li, Wei-Chan Hng Abstract The present study applied cmputatinal fluid dynamics t a type f cntemprary antitank missile capable f entering int a unique tp-attack mde, and explred the differences in the aerdynamic prperties f the missile with its tailfins swinging at varius angles. Simulatin results indicated that the drag cefficient increased with the angle f attack, the swing angle f the vertical tailfins, and the negative swing angle f the hrizntal tailfins. The lifting effect frm the swinging f the vertical tailfins was bserved t cntribute.5% f the ttal lift, and the hrizntal tailfins prvided a higher lift when psitined in negative swing angles. As the angle f attack was increased, the lift cefficient als increased, and culd be presented in a linear functin invlving the angle f attack and the swing angle f the tailfins: C L = Φ(α,δh). When α = 5, δv =, and δh = t -, the lift-t-drag rati f the missile (C L /C D ) was apprximately 3. The eight wings in the middle sectin f the missile cntributed t apprximately 64.5% f the ttal lift, implying that an adequate number f middle fins prvide higher lift. When δv = and δh =, the stalling angle f attack f the missile was 4. The present study demnstrated frm the aerdynamic prperties f the missile that the missile had a high lift-t-drag rati and excellent flight stability, enabling it t scramble rapidly then dive in a tp-attack mde. Keywrds cmputatinal fluid dynamics, anti-tank missile, Mach number, drag cefficient, lift cefficient, stalling angle f attack I. INTRODUCTION A guide and cntrl system significantly increases the hit rate f anti-tank missiles. Cmbined with armr-piercing high-explsive warheads, the design effect f a single missile destrying a tank can be achieved. Current anti-tank missiles include the U.S. FGM-48 Javelin, AGM-4 Hellfire, FGM-77 Dragn, and BGM-7. The precisin and destructiveness f these missiles characterize them as the greatest threat t tanks. The hardware cmpsitin f anti-tank missile systems is generally divided int fur sectins: the guidance, warhead, actuatr, and prpulsin sectins. The exterir design f the missile bdy emphasizes aerdynamic characteristics in additin t structural strength. During missile flight, the crrespnding aerdynamics, such as the lift, drag, and mment that are prduced frm the air flw against the surface f the missile bdy, directly influence its flight attitude, stability, and handling r peratinal characteristics. Therefre, Chun-Chi Li, Department f Mechanical and Aerspace Engineering, Chung Cheng Institute f Technlgy / Natinal Defense University, Taiwan, ROC. Email id: davidli5667@gmail.cm Wei-Chan Hng, Master Prgram f Mechanical Engineering, Chung Cheng Institute f Technlgy / Natinal Defense University, Taiwan, ROC missiles with different functins invlve. Analysis methds fr determining the aerdynamic parameters f flying bjects include aerdynamic parameter values measured by cnducting wind tunnel experiments and semi-empirical methds similar t thse f the U.S. Air Frce Missile DATCOM. The calculatin efficiency f cmputers has significantly increased with the develpment f cntemprary cmputer technlgy; therefre, cmputatinal fluid dynamics (CFD) simulatin has gradually becme the fcus f aerdynamic calculatins, and can facilitate wind tunnel experiments and subsequently decrease research csts. Tuncer et al. [] cnducted numerical simulatins invlving subsnic velcity missile bdies f different canard-tail aerdynamic distributins. The experiments examined an angle f attack α ranging frm t 6, calculated the relatinship amng α, nrmal frce cefficient C N, and pitching mment cefficient C M, and bserved the lcatin in which airflw creates separatin, recnnectin, and vrtex phenmena. Champigny [2] examined the lcatins in which the bundary layer, vrtex, and air separatins ccur because f the air viscsity effect, and selected fur turbulence mdels t cnduct a numerical simulatin invlving missile bdies with fins. Amng these mdels, the Spalart-Allmaras turbulence mdel has undergne lng-term empirical verificatins, and is adaptable t the majrity f existing cmplex flw fields, particularly t rise and drag prblems f missile bdies with fins. DeSpirit [3] adpted the CFD numerical simulatin and selected the Spalart-Allmaras turbulence mdel t calculate the aerdynamic effects f varius α fr missile bdies cnfigured with and withut fins. DeSpirit subsequently cmpared the results t that f the wind tunnel experiment, and bserved an errr within 5%. This study calculated the aerdynamics f an existing and active 3D anti-tank missile (Fig. ) t examine the aerdynamic characteristics f a missile bdy at different flight attitudes. The missile has a unique tp-attack mde that enables it t scramble t a cnsiderable height in a relatively shrt distance and then dive n the thinnest armred spt f a tank. The eight middle wings are als wrthy f nte, because this is the highest number seen n cntemprary antitank missiles. This feature was f interest t the present authr, particularly fr its aerdynamic prperties and whether it was purpsefully designed fr the tp-attack mde. Accrding t the data f Harris and Slegers [4] regarding this missile, when the flight trajectry adpts a tp-attack mdel, the range is apprximately 2, m and the flight time is apprximately 6 s. The velcity f the missile after detaching https://di.rg/.7758/eirai.f27 65
Int'l Cnference n Research & Innvatin in Cmputer, Electrnics and Manufacturing Engineering (RICEME-7) Feb. 2-3, 27 Bali (Indnesia) frm the launch tube is 3 m/s, and the pitch angle is θ = 8. Harris and Slegers prvided five perfrmance curve graphs, respectively presenting the height-length plt (H-L plt), flight velcity-length plt (V-L plt), α-time plt (α-t plt), θ-time plt (θ-t plt), and the cntrl tail fin deflectin-time (δ-t) plt. Analysis was cnducted n the infrmatin prvided by Harris and Slegers, and it was discvered that the pwer f the missile regarding velcity riginates frm the engine at the rear f the missile bdy. The mass f the slid prpellant in the engine is a cnstant value, and limits the basic flight range r length and velcity. Regardless f any attack mdel r ballistic trajectry, the flight velcity is apprximately between.3 and.5 M. Regarding the flight attitude, the perid between the missile s detachment frm the launch tube and the activatin f the guide and cntrl system is the preliminary trajectry. This perid is uncntrlled and, thus, exhibits inferir stability. After the guide and cntrl system is activated, the trajectry is immediately directed tward the default trajectry, subsequently requiring greater cntrl. The primary attitude cntrl riginates frm the jet vane thrust vectr system f the engine. Substantial trajectry crrectins during this perid result in a significant variatin in α. When the engine has cmpleted functining and the missile bdy has entered the default trajectry, the subsequent attitude crrectin is cntrlled by the fur cntrl fins n the rear f the missile bdy. The tail fins cntinuusly crrect the trajectry path r attitude during stable flight. Data shw that unless lift is required, the cntrl system primarily maintains the flight attitude f the missile bdy at a lw α t decrease the negative effects caused by air resistance r drag. Therefre, the α f the missile during stable flight is maintained between and 5. The fur swept-back cntrl tail fins f the missile are designed t be crss-shaped, and lift, drag, and lateral frce are crrespndingly prduced during flight based n the deflectin and swing f the cntrl tail fin. Rlling mment, pitching mment, and yawing mment are prduced in crrespndence t the center f pressure (CP). These three types f mment can alter the flight attitude f the missile bdy. Variatins in the tail fin deflectin angle directly affect the air flw field, resulting in different aerdynamic effects; therefre, the abve factrs must be cnsidered during calculatin and simulatin. The tail fin cmprises the Y-directinal vertical tail fin and the Z-directinal hrizntal tail fin. Based n the δ-t curve f the cntrl tail s deflectin angle in [5], the deflectin angle f the vertical and hrizntal tails are apprximately cntrlled between - t. This study defined the deflectin angle f the vertical tail fin as δ v and that f the hrizntal tail fin as δ h. Cunterclckwise rtatin indicates a psitive value, as shwn in Fig. 2. Regarding literature n wind tunnel experiments fr this anti-tank missile, Lei et al. [5] cnducted a series f wind tunnel experiments n six types f missile fin distributins with an Mach numbers between.3 and.5. The results indicated that a distributin f eight mid-fins and fur tail fins exhibited superir stability in the subsnic velcity range f the experiment. In additin, a.4-m experiment was cnducted at α =, and Lei et al. acquired a drag cefficient f C D =.29.Based n these results, this study emplyed the fllwing flight criteria fr anti-tank missiles: M =.3~.5, α = ~5, δ v = ~, and δ h = - ~. These criteria were used t examine the aerdynamic characteristics f missiles. Relevant infrmatin is further prvided as reference fr future develpment f nvel anti-tank missiles. Fig. Anti-tank missiles f this study[] Fig 2. The cntrl tail fin swing schematic II. PROBLEMS AND METHODS A. Gverning Equatin and Numerical Methds The gverning equatins are the Reynlds averaged Navier-Stkes equatins, the cnservatin can be expressed as fllws U F G H F G H () t x y z x y z In slving equatin (), cnvectin terms (F,G,H) are calculated by AUSM+ scheme, while viscsity and diffusin flux terms (F ν, G ν, H ν ) are calculated using the central difference methd. Discrete space terms are t frm a grup f rdinary differential equatins fllwed by time integratin t btain the numerical slutin. Turbulence mdel adpted the Spalart-Allmars equatin. The cnditin f inlet bundary and utlet bundary shuld be set at pressure-far-field cnditin and pressure-utlet cnditin, respectively. B. Grid System and Numerical Cde Validatin This study set the cmputatinal dmain inlet as ne times the length f the missile extended frm the tip f the missile, and the distance between the rear f the missile bdy and the cmputatinal dmain utlet as 2.5 times the length f the missile. The surface grid and varius parts f the missile bdy are identified in Fig. 3a. The cylinder diameter was tw times the length f the missile, and the cmputatinal dmain is shwn in Fig. 3b. T verify the accuracy f the numerical simulatin, this study emplyed the wind tunnel experiment data used in [5] as cmparative data fr simulatin verificatin. https://di.rg/.7758/eirai.f27 66
Int'l Cnference n Research & Innvatin in Cmputer, Electrnics and Manufacturing Engineering (RICEME-7) Feb. 2-3, 27 Bali (Indnesia) under M =.3, α = 5, δv =, and δh = ; and 3_5 "-~" dentes that M =.3, α = 5, and δv =, where δh swings frm - t. The rigin lcatin is at the tip f the missile. This study divided the upper and lwer sectins f the missile bdy int fur primary sectins with the axis and mid-fin as a benchmark (Fig. 5). The upper sectin f the missile bdy is the leeward side, which was further divided int Sectins I and II; and the bttm sectin f the missile bdy is the windward side, which was further divided int Sectins III and IV. When M =.4 and α =, the missile bdy s δv = and δh =, and experimental CD =.29. Regarding lattice pint calculatins, the cncentratin f lattice pints were increased n the surface f the missile bdy wall, between the mid-fin and the tail fin, at the bundary layer, and in the rear vrtex area at the bttm f the missile. Nine grid number systems were used t cnduct prgram verificatin. The calculatin results were similar t the experimental drag cefficients, as shwn in Fig. 4. Fr superir calculatin efficiency, tw millin grids were used as the grid system fr simulatin. Fig 5. The anti-tank missile partitin schematic diagram III. RESULTS AND DISCUSSION A. An Examinatin f the Drag Cefficient When M and δv are fixed, δh is adjusted as -, -5,, 5, and fr simulatin. The results shw that the greater the angle is, the greater the CD. When α =, CD is the same when the psitive and negative δh are identical, and the representatin in the figure is subsequently symmetrical (Fig. 6). When α is psitive, and the psitive and negative δh have identical angles, a negative δh pssesses a greater drag cefficient than a psitive δh des. Furthermre, the greater the angle is, the greater the CD, as shwn in Fig. 7. Fig. 8 shws the calculatin results f 5_5 "-~". Regarding the pressure distributin n the surface f the missile bdy, when air flw enters Sectin I, air flw clser t the junctin wall surface between the tail fin and the missile bdy is cmpressed, and the pressure in this sectin is subsequently increased. This indicates that a prtin f the missile s kinetic energy is transfrmed int pressure, and subsequently prduces drag. A different δh als results in different air flw cmpressin situatins near the tail fin sectin, subsequently prducing different pressure gradients. When δh =, 5, and, air flw is mre likely t flw smthly past the surface f the tail fin wall; thus, the area affected by high-pressure is smaller. The maximum pressure is apprximately 4, Pa, and the area affected by high pressure significantly expands when δh = -5 and -. When δh = -5, the maximum pressure n the cnjining wall surface f the tail fin and the surface f the missile bdy exceeds apprximately 5, Pa. When δh = -, the maximum pressure exceeds 7, Pa, indicating that mre kinetic lss ccurs when δh = -, prducing greater drag. Fig 3a. Anti-tank grid diagram Fig 3b. Schematic diagram f cmputatinal dmain Fig 4. The drag cefficient cmparisn verify the independence f the grid C. Mdel Parameter Explanatin The varius simulatin parameters fr the calculatin mdel are explained as fllws: The rder f arrangement is M, α, δv, and δh. Fr example, 3_5 indicates the flight cnditin https://di.rg/.7758/eirai.f27 67
Int'l Cnference n Research & Innvatin in Cmputer, Electrnics and Manufacturing Engineering (RICEME-7) Feb. 2-3, 27 Bali (Indnesia) B. An Examinatin f Lift Cefficients Fig. 9 shws that when M =.5, the lift cefficient increases alng with α. When δh is fixed, the swing angle r deviatin fr δv pssesses similar lift cefficients, and almst n influence is prduced, because the δv prjectin areas that are affected by lift shw little change. The lift cefficient is influenced by δh; therefre, when the swing angle is between - and, the lift cefficient underges a linear increase. The calculatin results fr 5_5_"~"_5 were selected, and an X-Y surface crss-sectinal view f the flw field was cnducted at Z =. The bservatins fr the pressure distributin f the upper- and lwer- sectins f the missile bdy are shwn in Fig.. The high-pressure sectin ccurs mre significantly at the windward side. With an α that des nt equal ccurs, air flw prduces a high-pressure sectin clse t the windward side f the mid-fin and a lw-pressure sectin clse t its leeward side, subsequently prducing lift. In additin, the pressure distributin curves f these three flw fields are extremely apprximate. Minr pressure distributin differences are nly bserved at the tail fin sectin. Fig. shws the lcatin n the missile bdy surface where the pressure data were retrieved. Fig. 2 shws the surface pressure distributin curves f the upperand lwer-surfaces n the missile bdy. Significant surface pressure differences are bserved near the head and the mid-fin f the missile. In additin, the pressure n the windward side f the missile bdy exceeds that f the leeward side. This pressure difference between the upper- and lwer-sides results in an up-ward lifting effect f the missile bdy; that is, the lift. The surface pressure curve in Fig. 2 shws that, regarding the simulatin results f 5_5_"~"_5, sectins aside frm r in frnt f the tail fin exhibit n upper- r lwer-surface pressure curve distributin differences. Only minimal pressure changes ccur at the tail fin sectin. Table I shws the calculatin results f the missile lift fr varius cmpnents at 5_5_"~"_5. The lift effect caused by δv accunts fr nly.5% f the influence n the ttal lift. Therefre, δv has an insignificant influence n the lift cefficient. M=.5 Fig 6. Drag cefficient plts (M=.3, α=,δv= ~,δh=- ~ ) Fig 7. Drag cefficient plts (M=.5,α=5,δv= ~,δh=- ~ ) 2 2 = _ v= = _ v=5 = _ v= =2.5 _ v= =2.5 _ v=5 =2.5 _ v= =5 _ v= =5 _ v=5 =5 _ v=.5 CL.5 -.5 -.5-5 h 5 Fig 9. lift cefficient in M =.5 Fig 8. The static pressure cntur f the hrizntal tail distributin (5_5 "-~") https://di.rg/.7758/eirai.f27 68.5.5 - - -
Int'l Cnference n Research & Innvatin in Cmputer, Electrnics and Manufacturing Engineering (RICEME-7) Feb. 2-3, 27 Bali (Indnesia) C. Stalling Angle f Attack Regarding the stalling angle f attack f the missile, an analysis was cnducted t explre its relatinship with the lift cefficient, specifically fr the speeds f.3 m,.4 m, and.5 m when the angle f attack α = 5 and the swing angles f bth vertical (δv) and hrizntal (δh) tailfins are (as shwn in Fig. 3). The results revealed that in the three scenaris, stalling ccurred at apprximately α = 4. The curve f lift suggested that greater lift culd be btained thrugh either a greater speed r a greater angle f attack. Differentiating lift with angle f attack (dfl/dα) achieved the curve f lift derivative illustrated in Fig. 4, frm which the derivative (dfl/dα) was bserved t diminish with the increase in angle f attack. This indicated that in a higher angle f attack, particularly when α = 4, the lift reached its maximum. Cntrarily, when the angle f attack exceeded 4, (dfl/dα) < and the lift started t decrease. Hence, the ideal stalling angle f attack f the antitank missile was determined t be 4. Fig. The static pressure cntur (5_5_"~"_5).3M~.5M Stall Angle-Lift Cef. 5.3M.4M.5M 4 CL 3 2 Fig.Schematic diagram f surface pressure data acquisitin 5_5_"~"_5 Surface Pressure Distributin 2 Mdel 5_5 5 Up 5_5_5_5 Up 5_5 5 Up 5_5 5 Bttm 5_5_5_5 Bttm 5_5 5 Bttm Pressure(Pa) 2 3 4 5 6 Fig 3.The plts f the liftfrce cefficients Lift Slpewith attack angles 6 -.3M.4M.5M 5 4.2.4.6 X (m).8 dfl/d -2-3.2 3 2 Fig 2. The static pressure cntur f missile surface (5_5_"~"_5) TABLE I. LIFT FORCE OF MISSILE (5_5_ " ~ " _5 ) Term 5_5 5 5_5_5_5 5_5 5 29.2 29.2 29.9 Head 7.7 7.88 7.56 Cylinder -4.3-4.6-4.45 Back -.39 -.39 -.4 Win- 7.57 7.65 7.72 Win-2 35.87 35.82 35.76 Win-3 9.76 9.66 9.57 Win-4 -.2 -.2 -.2 Win-5 8.66 8.77 8.89 Win-6 36.3 36.6 36.7 Win-7 9.95 9.86 9.76 Win-8 -.65 -.95 -.34 Fin- -7.4-7.6-7.8 Fin-2.42.39 -.4 Fin-3-7.2-7.8-7.3 Fin-4 229.28 228.53 226.92 Net https://di.rg/.7758/eirai.f27-2 3 4 5 Fig 4.The plts f differentiating lift with angle f attack IV. CONCLUSIONS Based n the previus cntent, this study presents the fllwing cnclusins. When α = and M and δv are fixed, adjusting δh t a greater angle prduces a greater drag cefficient. In additin, the drag cefficients are identical when the psitive and negative angles are identical. When α is psitive, a negative δh prduces a greater drag cefficient than that f a psitive δh. In additin, a greater δh results in a greater drag cefficient. Therefre, when cnducting missile bdy 69
Int'l Cnference n Research & Innvatin in Cmputer, Electrnics and Manufacturing Engineering (RICEME-7) Feb. 2-3, 27 Bali (Indnesia) flight attitude cntrl, turning the hrizntal tail fin tward a negative swing angle prduces greater drag. When δ v and α are fixed, a greater lift is prduced at δ h = -. When δ h = - swings t a psitive angle, the lift cefficient exhibits a linear decrease. When α = and δ h >, negative lift is prduced, subsequently resulting in a decrease in the missile bdy s flight height. Therefre, when lift is required, δ h shuld be adjusted t a negative angle, because the greater the negative swing angle is, the greater the lift. Furthermre, the influence f the δ v n lift is insignificant, accunting fr nly.5% f the influence n the ttal lift. When α and δ h are identical, their lift cefficients are als identical. Lift cefficients can be perceived as a linear functin created by α and δ h ; that is, C L = Φ(α,δh). When α = 5, δ v =, and δ h = t -, the lift-t-drag rati f the missile (C L /C D ) was apprximately 3. The eight fins in the middle sectin f the missile cntributed t apprximately 64.5% f the ttal lift, implying that an adequate number f middle fins prvide higher lift. When δ v = and δ h =, the stalling angle f attack f the missile was 4. The present study demnstrated frm the aerdynamic prperties f the missile that the missile had a high lift-t-drag rati and excellent flight stability, enabling it t scramble rapidly then dive in a tp-attack mde. ACKNOWLEDGMENT The authr wuld like t thank the Ministry f Science and Technlgy f the Republic f China fr financially supprting this research under Cntract N. MOST 3-222-E-66-9- REFERENCES [] I. H. Tuncer, M. F. Platzer, and R. D. VanDyken, A cmputatinal study f a clse-cupled delta canard-wing-bdy cnfiguratin, in 996 4 th AIAA Applied Aerdynamics Cnf., New Orleans, LA, 96-24. https://di.rg/.254/6.996-244 [2] P. Champigny, P. d'espiney, M. Bredif, H. Brussard, and J. Gillybeuf, Numerical simulatin f vrtex flws arund missile cnfiguratins, in 23 RTO AVT Symp., Len, Nrway, pp. -3. [3] J. DeSpirit, Base pressure cmputatins f the DERA generic missile wind tunnel mdel. Army Research Labratry, Maryland, U.S.A, pp.-2. 25 [4] J. Harris, and N. Slegers, Perfrmance f a fire-and-frget anti-tank missile with a damaged wing, Mathematical and Cmputer Mdelling, vl. 5, pp. 292-35, 29. https://di.rg/.6/j.mcm.29.2.9 [5] J. M. Lei, and J. S. Wu, An experiment investigatin f the aerdynamic characteristic fr a multi-wing light anti-tank missile, ACTA Armamentarii, vl. 26, n. 5, pp. 79-7, 25. Chun-Chi Li Assciate prfessr, Department f Mechanical and Aerspace Engineering, CCIT, NDU, Tauyuan Cunty, Taiwan, ROC, 29-present. Research field in CFD, Heat and mass transfer, Prus media, Shck waves. https://di.rg/.7758/eirai.f27 7