Investigations on Missile Configuration Aerodynamic

Trans. Japan Soc. Aero. Space Sci. Vol. 57, No. 4, pp. 210–218, 2014

Investigations on Missile Conﬁguration Aerodynamic Characteristics for Design Optimization

By Nhu-Van NGUYEN, Maxim TYAN, Jae-Woo LEE and Yung-Hwan BYUN

Department of Aerospace Information Engineering, Konkuk University, Seoul, Korea

(Received February 4th, 2013)

The integrated missile design optimization process is proposed by implementing the aerodynamics database (Aero DB) and tactical missile design (TMD) spreadsheet to obtain a quick and relatively accurate optimal air intercept missile configuration at the conceptual design stage. The Aero DB is constructed to replace an existing aerodynamics analysis module in the TMD spreadsheet and to provide stability and control coefficients as constraints for improving missile range performance based on the body-wing-tail configuration baseline. Sensitivity analysis is performed on an entire missile geometry and flight condition variables to eliminate the small effects of design variables on missile range and constraints under a PHX ModerCenterÒ 10.1 integration environment. The optimal missile configuration shows 27.8% improvement in total range compared with a body-wing-tail configuration baseline while all constraints are satisfied. The proposed integration of the missile design program using Aero DB demonstrates more accurate and reliable results which are validated by high-fidelity analysis ANSYS Fluent 13Ò on the optimal missile configuration compared with TMD aerodynamics analysis results. The maximum difference between ANSYS Fluent and Missile DATCOM is 11.76% at 10 degrees of AoA compared with 37.97% for TMD aerodynamics analysis and ANSYS Fluent difference.

Key Words: Aerodynamics Database, Air Intercept Missile (AIM) Aerodynamics, Missile DATCOM 97, Missile Design Optimization

Nomenclature h: launch altitude tdome: dome thickness : side slip angle tmotor: motor thickness : roll angle ðt=cÞW : wing max. thickness ratio a: aileron deflection angle ðt=cÞtail: tail max. thickness ratio e: elevator deflection angle SW : wing area r: rudder deflection angle WL: launch weight W : wing taper ratio Wboost: boost weight tail: tail taper ratio Wcruise: cruise weight AoA: angle of attack XCG: longitudinal center of gravity ARW : wing aspect ratio XW : wing longitudinal location ARtail: tail aspect ratio Xtail: tail longitudinal location CA: axial force coefficient AIM: air intercept missile CL: lift coefficient AAM: air-to-air missile CN : normal force coefficient SQP: sequential quadratic programming Cm: pitching moment coefficient SM: static margin CDo: zero-lift drag coefficient TMD: tactical missile design Cl: static lateral derivative Cn: static directional derivative 1. Introduction Cm: static pitching derivative Dbody: missile body diameter The U.S. Air Force Missile DATCOM Ver. 97 software1) Dhemi: nose bluntness is used widely in stability and aerodynamic analyses for Isp: specific impulse wing-bodies and tails.2) Basically, Missile DATCOM is an L=D: lift to drag ratio engineering level computer code that predicts the aerody- Lmissile: missile length namic forces, moments, and stability derivatives of axisym- LN : nose length metric and non-axisymmetric missile configurations for a M: mach number wide range of attack angles and Mach numbers. The capa- Mi: initial Mach number bilities of missile DATCOM are comprehensive in comput- Mter: terminal Mach number ing a wide range of flight conditions from subsonic to hyper- sonic speeds, and control surface deflections from 35 to 35 Ó 2014 The Japan Society for Aeronautical and Space Sciences Jul. 2014 N.-V. NGUYEN et al.: Investigations on Missile Configuration Aerodynamic Characteristics for Design Optimization 211 degrees.1) Moreover, Missile DATCOM is also used for pre- dicting and evaluating missile aerodynamic characteristics at high angles of attack up to 90 degrees.3,4) In addition, Missile DATCOM is considered to be an aerodynamic module for various missile conceptual design applications such as the preliminary design of liquid-propellant missile system with single and multi-objective optimization5,6) and for supersonic missile preliminary design7) in which it provides faster and more competitive results compared to the other aerodynamic code-Aerodsn.6) Nowadays, missile aerodynamic databases are used as a very important module for missile simulation and autopilot.8) Besides that, aerodynamic databases are widely applicable for missiles, aircraft conceptual design and simulation,8,9) and wind-induced pressure time series on the envelope of various low buildings.10) There are many tools to construct the aerodynamic Fig. 1. Aero DB construction process for an arbitrary missile. databases which are wind-tunnel test,9) and to use high- fidelity analysis for some critical lateral jet missile conditions.11) However, to construct aerodynamic database used for missiles, aircraft simulation and autopilot require large computational cases and time to interpolate accurately dur- ing different flight conditions. Hence, the computation cost and accuracy of problem must be compromised before pro- Fig. 2. Body-wing-tail missile configuration for missile DATCOM ceeding to construct the database for applications. There- validation.12) fore, the aerodynamic database (Aero DB) program is developed for arbitrary missile by implementing the missile DATCOM 97 as a core analysis. The pre- and post-processes 2.1. Aero DB program pre-process are programed by MATLABÒ to arrange inputs and outputs The pre-process is coded to read arbitrary missile config- into the right format for the flight simulation and missile uration and flight condition and save automatically into the conceptual design optimization. missile DATCOM input format. The Mach number, angle of In this study, the validation of body-wing-tail configura- attack and sideslip angle calculation range are specified in tion is performed on Missile DATCOM comparing with this stage to create Aero DB in the next step. an experimental data. The short and medium range missile 2.2. Execution and checking process medium range configuration are selected to generate Aero Missile DATCOM 97 is the aerodynamic analysis code in DB and to investigate missile aerodynamic characteristics. the Aero DB program. The validation of Missile DATCOM The missile conceptual design optimization process imple- 97 and the checking process are presented to ensure that the menting Aero DB program is proposed and demonstrated accurate aerodynamics data and the correct output format by maximizing a total range of a baseline missile body- are provided for the next application. wing-tail configuration. The validation of optimal missile 2.2.1. Validations of Missile DATCOM 97 configuration is performed using the high-fidelity analysis The efforts are performed to reproduce the validation ANSYS Fluent to demonstrate the effectiveness of the pro- of Missile DATCOM 97 using a body-wing-tail configura- posed missile design optimization process. tion as shown in Fig. 2 with the experimental data and AeroPrediction 98 (AP98).12–14) The AeroPrediction 98 2. Missile Aero DB Program Development (AP98) or current version AP0915) released in 2009 is a semi-empirical code enhanced by an improved boundary- An accurate aerodynamics database for an arbitrary mis- layer displacement model and refinement of several existing sile is extremely important and necessary for missile guided methods.15) The normal force and pitching moment coeffi- simulation, trajectory and design. Therefore, the missile cients of body-wing-tail configuration analysis results show Aero DB program is developed and presented. The Aero good agreement with the experimental data and AP98, and DB construction process is shown in Fig. 1. The Aero DB the maximum error between the predicted data and experi- program is composed of pre-process, execution and check- ment data is approximately 5.2%.13,14) The normal force ing, and post-process. The Aero DB program is written coefficient for body-wing-tail configuration validation is using MATLABÒ. Missile DATCOM is implemented as a presented in Fig. 3(a) in which a similar trend of Missile main analysis tool in the Aero DB program. In addition, DATCOM result is observed while comparing with the the investigations on aerodynamic characteristics of the experiment data and AP98. The pitching moment coefficient arbitrary missile are presented. comparison shows a right trend and good agreement with experiment data at less than 30 degrees of AoA in Fig. 3(b). 212 Trans. Japan Soc. Aero. Space Sci. Vol. 57, No. 4

40 0 Experiment DATCOM 97 -10 30 AP98 -20 N 20 m C C -30 Experiment 10 -40 DATCOM 97 AP98 0 -50 0 10 20 30 40 50 0 10 20 30 40 AoA (deg.) AoA (deg.) φ (a) CN at M =1.5 and φ =45° (b) Cm at M =1.5 and =45°

Fig. 3. Validation results for body-wing-tail conﬁguration baseline.

It shows a bigger gap while AoA is larger than 30 degrees Table 1. Calculation range of the medium range configuration. compared with AP98. However, it is acceptable for con- M 0.7 0.9 1.1 2.0 3.0 structing Aero DB and a missile conceptual design stage. AoA (deg) 40.0 17 values 40.0 Therefore, Missile DATCOM 97 is selected to construct (deg) 40.0 20.0 0.0 20.0 40.0 Aero DB to implement for missile simulation and design op- (deg) 16.5 0.0 16.5 timization. r (deg) 16.5 0.0 16.5 2.2.2. Checking process e The checking process is performed before reading and writing the output file correctly into aero databases, and Table 2. Calculation range of the short range configuration. RW DB is programmed in MATLAB. The RW DB consists of checking output format to detect the correct format form M 0.7 0.9 1.1 2.0 3.0 and reading into Aero DB. If the RW DB detects a different AoA (deg) 40.0 17 values 40.0 output format, users must go back to adjust inputs for (deg) 40.0 20.0 0.0 20.0 40.0

Missile DATCOM. r (deg) 15.0 0.0 15.0

2.3. Aero DB program post-process e (deg) 15.0 0.0 15.0

The post-process is executed using the RW DB to write a (deg) 15.0 0.0 15.0 the missile outputs into the right format for flight simulation and design optimization. The 17 available aerodynamic coefficients including the static and dynamics coefficients are presented in Aero DB. Aerodynamic coefficients characteristics are investigated.

14) 3. Medium and Short Range Configuration Aero DB Fig. 4. Medium range missile configuration. Constructions 3.1. Medium range configuration The air-to-air missile is broadly classified into two The detailed configuration of the medium range type con- groups. The first group is designed to engage opposing figuration14) and flight conditions in Table 1 and Fig. 4 are aircraft at ranges of less than 30 km and are known as a modeled into the Missile DATCOM in order to generate short-range or within visual range missiles. Most short range the medium range configuration aerodynamic database. A missiles use infrared guidance called heat-seeking missiles. turbulent boundary layer and full base drag conditions are The second group are beyond visual range missiles includ- assumed. Due to the requirements of flight simulation of ing medium and long range missiles which tend to depend the medium range configuration aerodynamics data, this on radar guidance. Therefore, the short range medium range study intends to build an aero-database of the medium range configuration and medium range short range configura- configuration with detailed configuration of medium range tion14) are selected to test the Aero DB program and to configuration for several critical flight conditions and for investigate aerodynamics characteristics. The calculation different bank angles. Additionally, the fin deflections ranges for the medium and short range configuration Aero are conducted with a range from 16:5 to 16.5 degrees DB construction are shown in Tables 1 and 2, respectively. and a Reynolds number of 2 106 per foot. The control surfaces of medium range configuration consist In Fig. 5, three aerodynamic coefficients (the normal- of rudder and elevator. The short range configuration is force, pitching-moment and axial-force coefficients) are composed of rudder, elevator and aileron surfaces. shown at an elevator deflection of 0 with various Mach numbers ranging from 0.7 to 3.0. The rest of the aerodynamic Jul. 2014 N.-V. NGUYEN et al.: Investigations on Missile Configuration Aerodynamic Characteristics for Design Optimization 213

2.5 M=0.7 M=0.9 M=1.1 2 M=2.0 M=3.0 Fig. 6. Short range missile conﬁguration.14)

A 1.5 C The discontinuity around 30 degrees, which appears from

1 high subsonic up to Mach number of 1.1 shown in Fig. 5(a), does not reﬂect the real missile aerodynamics correctly. The Missile DATCOM utilizes two distinct methods. The modi- 0.5 -40 -20 0 20 40 ﬁed Allen and Perkins’ method is implemented for AoA AoA below 30 degree, and the Jorgensen’s slender body theory (a) 16,17) CA at various Mach numbers is used for AoA above 30 degree. Hence, Missile

100 DATCOM results presenting the discontinuity around 30 M=0.7 degrees is due to the switchover in two method calculations. M=0.9 M=1.1 However, the axial force coeﬃcient predicted by Missile 50 M=2.0 DATCOM still captures the tendency of missile aerody- M=3.0 namic characteristics. When Mach number increases up to

N 0

C 2.0 and 3.0, the main drag components are the wave drag that has a reducing tendency based on potential theory and

-50 the leading-edge bluntness that has a small reduction while increasing Mach number. Therefore, the trend of axial force coeﬃcient is seen at Mach number of 2.0 and 3.0, as shown -100 -40 -20 0 20 40 in Fig. 5(a). AoA The normal force coeﬃcient increases when the AoA

(b) CN at various Mach numbers increases from 0 to 40 degrees, as shown in Fig. 5(b). How- ever, the normal force coefficient at the supersonic regime is 100 M=0.7 lower than at the subsonic and transonic regime. The reason M=0.9 is that the stronger shocks occur at the supersonic flow; M=1.1 therefore the normal force is reduced behind the stronger 50 M=2.0 M=3.0 shocks. The pitching moment coefficient shows stability in the longitudinal direction. When the nose of the medium m 0 C range configuration is up, the pitching moment coefficient is negative, as shown in Fig. 5(c). -50 Three important aerodynamic coefficients, axial, normal and moment coefficients, are presented and analyzed for dif- -100 ferent flight conditions. These coefficients show the right -40 -20 0 20 40 AoA trend and behavior of the medium range configuration. (c) Cm at various Mach numbers The remaining fourteen medium range configuration aerodynamic coefficients are stored in the database with a set Fig. 5. Aerodynamic characteristics of medium range type configuration. of different sideslip angle, elevator and rudder. 3.2. Medium range missile short range configuration coefficients are also calculated with the same range of Mach The detailed short range configuration14) and flight condi- numbers, AoA and control surface deflection. tions in Table 2 and Fig. 6 are modeled into the Missile In Fig. 5(a), the axial force coefficients have similar DATCOM to predict and construct the aerodynamic data- tendencies with body-wing-tail configuration results13) from base. A turbulent boundary layer and full base drag condi- subsonic to supersonic regimes. The medium range config- tions are assumed. Additionally, the fin deflections are con- uration produces the lowest drag at Mach number of 0.7 ducted from 0 to 15 degrees and the Reynolds number is 2 due to the main effects of skin friction, subsonic pressure 106 per foot. drag and leading-edge bluntness considered in the Missile In Fig. 7, three aerodynamic coefficients (the normal- DATCOM method16,17) and then, it increases up to the Mach force, pitching-moment and axial-force coefficients) are number of 0.9 in which the wave drag starts having a small shown at the elevator deflection of 0. The axial force coef- contribution on total drag when shocks occur on the missile. ficient has a similar behavior with medium range configura- At the Mach number of 1.1, the axial force coefficient tion. However, the highest axial force coefficient variations reaches the highest values. This is because the leading-edge are at Mach number of 2.0. The discontinuity around 30 bluntness drag increases and the wave drag contributes the degrees of AoA can be seen clearly up to Mach number of large portion in the total drag at this Mach number. 1.1 in Fig. 7(a). That is due to the switchover between 214 Trans. Japan Soc. Aero. Space Sci. Vol. 57, No. 4

35 1 M=0.7 M=0.9 Wing-body-tail configuration M=1.1 30 Short range configuration 0.8 M=2.0 M=3.0 25

0.6 20 N A C C 15 0.4 10

5 0.2 -40 -20 0 20 40 AoA 0 0 5 10 15 20 25 30 35 40 45 (a) C at various Mach numbers A AoA (deg.)

50 Fig. 8. CN comparison at M ¼ 1:5 and ¼ 45 for body-wing-tail and M=0.7 short range conﬁguration. M=0.9 M=1.1 M=2.0 M=3.0 The short range conﬁguration is designed and aimed with

N 0 the most sophisticated radar guided air to air missile (AAM) C and the aerodynamics performance as well. The short range configuration has the same length as the body-wing-tail configuration. However, the wing and fin of the short range configuration are designed to provide better performance -50 -40 -20 0 20 40 and allow easy installation to fighters. The short range con- AoA figuration aerodynamic charateristics are investigated and (b) CN at various Mach numbers compared in normal force coefficient at Mach of 1.5 and roll angle of 45 degrees, as depicted in Fig. 8. Therefore, it is 300 M=0.7 concluded that the short range configuration aerodynamic 200 M=0.9 characteristics have good agreement and reasonable results M=1.1 compared with the prior body-wing-tail configuration and M=2.0 100 M=3.0 published data.

m 0 C 4. Aero DB Program Application for Missile Concep- -100 tual Design Optimization -200 4.1. Missile design optimization process using Aero DB -300 -40 -20 0 20 40 Aero DB is applied for the air-to-air missile conceptual AoA design optimization process as shown in Fig. 9. The analysis (c) Cm at various Mach numbers solver is composed of Aero DB constructed from Missile Fig. 7. Aerodynamic characteristics of the short range configuration. DATCOM and the TMD Spreadsheets.18) The TMD Spread- sheet, which is based on semi-empirical equations, consists of aerodynamics, propulsion, weight, performance and tra- two calculation methods mentioned in the medium range jectory analysis modules. TMD is quite appropriate for the configuration results. Although it does not reflect the real conceptual design of missiles as it obtains conceptual results aerodynamics correctly around that switchover point, it is quickly and effectively. The validation is performed for the still able to capture the trend of the axial force coefficient. body-wing-tail configuration in Fig. 3 at launch conditions The axial force coefficient has a gradual change at super- which are Mach 0.8; altitude of 20,000 ft; flight range of sonic regime, because of wave drag that has main contribu- 7.7 n miles, exceeding the requirement of 6.7 n miles by tion on total drag in this supersonic regime. 15%. The body-wing-tail configuration baseline achieves The normal force coefficient has a similar behavior with the required flight range of 6.7 n miles within a time that medium range configuration, as shown in Fig. 5(b). It is 14% shorter than the required time of flight (21 vs. increases when AoA increases from 0 to 40 degrees and 24.4 s).18) Mach number increases from subsonic to transonic regime. The Aero DB is stored and called to replace an aerody- However, the normal force coefficient at the supersonic namics analysis module in the TMD Spreadsheet and to pro- regime is lower than at the subsonic and transonic regime vide stability and control coefficients to an optimizer as due to stronger shocks occurring in front of the nose of shown in Fig. 9 for missile trajectory, propulsion and the missile. The pitching moment coefficient also shows dynamics analysis in the TMD Spreadsheet at different stability in the longitudinal direction, as shown in Fig. 7(c). flight conditions including boost, sustain and coast stage Jul. 2014 N.-V. NGUYEN et al.: Investigations on Missile Configuration Aerodynamic Characteristics for Design Optimization 215

Dbody h

Mter

Wboost Others

Wcruiset

Wboost:Dbody

Mlaunch

WL:Dbody

Fig. 10. Total range sensitivity analysis.

Dbody

XCG

Fig. 9. Missile design optimization process. Lmissile

SW after launching from a fighter. The lift, drag and stability X coefficients are estimated from Aero DB using Table lookup tail as shown in Fig. 9 which implements the linear interpola- XW tion technique between nearest points through Mach num- Others ber, side slip angle, control deflection angle, and angle of XCG:Xtail attack variables provided from the flight conditions. LN The sensitivity analysis module is implemented to eliminate small effects of design variables on objective function XCG:Dbody and constraints. The optimizer is integrated to an analysis solver to seek an optimum missile configuration with an Fig. 11. Sustain drag coefficient sensitivity analysis. improvement in performance characteristics. The integration of missile design optimization is completed in PHX (XCG) has a 16% effect on drag coefficient. The remaining 19) ModelCenter 10.1. The high-fidelity analysis ANSYS effects including missile length, wing area (SW ), tail location 20) Fluent is implemented to validate aerodynamics analysis (Xtail), and wing location (XW ) are considered as shown in results for an optimum configuration. Fig. 11. 4.2. Air-to-air missile sensitivity analysis 4.3. Missile design formulation Sensitivity analysis is performed on 24 variables includ- The specific mission profile for the body-wing-tail config- ing missile characteristics and configuration using a Latin uration baseline is shown in Fig. 12 which is divided into hypercube and orthogonal method in ModelCenter 10.119) boost, sustain and coast phases. The propulsion, structure, with 300 design points to address the effects of design var- trajectory and dynamic analysis module are maintained to iables on performance and stability parameters such as complete this given mission profile in the TMD Spread- boost, sustain and coast range, pitching, directional, and sheet.18) Only aerodynamics and stability coefficients are lateral moment coefficient. Sensitivity analysis helps to derived from Aero DB. determine main design variables affecting the objective The total range including boost, sustain and coast stages is and constraints function. selected as an objective function to be maximized. The aer- The most effective variable for total range parameter is a odynamics and stability constraints are listed as follows for missile diameter at 66% which causes a large increment in boost, sustain and coast stage conditions. The design varia- drag while increasing missile diameter. It effects the range bles are reduced to 16 variables after the sensitivity analysis of each boost, sustain and coast range. Other factors include process in which small sensitivity of the variables and launching altitude (h), terminal Mach (Mter), boost weight launch speed are removed from formulation as shown in (Wboost), nose length, cruise weight (Wcruise), launch Mach Table 3. The lower and upper bounds are set from 20% number (Mlaunch), and launch weight (WL) which have a from a baseline for design space. smaller sensitivity to total range of missile as shown in Maximize:

Fig. 10. RangeTotal ¼ RangeBoost þ RangeSustain þ RangeCoast The drag for the sustain condition mainly eﬀects on mis- Subject to sile diameter (61%). The missile CG longitudinal location 216 Trans. Japan Soc. Aero. Space Sci. Vol. 57, No. 4

Sustain stage 4.4. Optimizer solver Level out AoA=2~3 deg. The Design Explorer algorithm, developed by Boeing and 19) Pitch-over integrated into PHX ModelCenter 10.1, helps to search on At high AoA an entire design space by surrogate models with sequential 21) Climb Coast stage optimization algorithm (SEOPT). The Design Explorer Launch: M=0.8 AoA=5~7 deg. altitude Pitch-up has been implemented and validated in many Boeing design At high AoA Boost stage applications such as high lift aerodynamics, multidiscipli- AoA=1~2 deg. Target impact at α ≈ 0 deg nary wing planform design, forming of aircraft wing skin, engine duct seal, and other products.21) The tolerances are Fig. 12. Missile mission profile.18) set up for objective functions, constraints and projected gradient which are 0.001, 0.001 and 0.01, respectively. The tol- Table 3. Air-to-air missile design optimum configuration. erances are set by the recommended convergence criteria of A baseline Optimum Unit the Design Explorer algorithm in the Model Center 10.1. Objective Total range 41,419 52,935 feet If there is no improvement in one of these tolerances, the program is terminated. Design variables h 20,000 19,000 feet 4.5. Optimum missile design configuration X 76.2 80.01 inches CG The optimum missile configuration is shown in Table 3 M 1.5 1.8 ter with 27.8% improvement in a total range including boost, L 143.9 172.68 inches missile sustain and coast conditions from 41,419 feet of baseline D 8 8.4 inches body to 52,935 feet of optimal configuration. Sixteen missile con- L 19.2 19.2 inches N figuration design variables are determined by an optimizer D 0.05 0.04 hemi for an improved range shown in Table 3. The 2D and 3D S 367.2 385.56 inches2 W optimum configuration comparison with a baseline are ðt=cÞ 0.044 0.0396 W presented in Figs. 13 and 14. AR 2.82 2.538 W The launching altitudes from fighters are close to a base- X 60.8 66.88 inches W line conditions. The optimum wing configuration becomes 0.175 0.193 W bigger in area and moves backward along to a missile longi- AR 2.59 2.46 tail tudinal direction. Hence, the lift coefficient over wing 0 0.375 tail increases to extend the range of each flight condition includ- X 125.4 151.67 inches tail ing boost, sustain and coast with a thinner airfoil in optimum ðt=cÞ 0.027 0.0284 tail missile configuration at 3.96% of maximum thickness ratio. Constraints Boost CDo 1.02 0.928 The optimum tail fin becomes larger than a baseline with a Coast CDo 1.14 0.9201 tapered tail fin and moves backward 27 inches in order to Sustain CDo 0.982 0.951 satisfy the stability constraints while wing area is increased L/D boost 1.376 1.386 and moved backward for better aerodynamics characteris- L/D sustain 1.381 1.398 tics. The optimum missile body is longer than a baseline L/D coast 0.888 1.002 at 30 inches. The optimum body fineness ratio, which is cal- Cm boost 0.0045 0.0262 culated as body length to diameter, becomes longer to pro- Cm sustain 0.0036 0.0273 vide better lift and less drag on the optimum configuration. Cm coast 0.0054 0.0221 The body fineness ratio is 18 which still lies between 5 to 25 Cl boost 0.0002 0.0429 for air-to-air missile guidance. The nose bluntness is Cl sustain 0.0025 0.0438 reduced to 4% compared to 5% as a baseline value. It re- Cl coast 0.0061 0.0407 duces the body drag with a smaller nose bluntness as shown Boost range 5,092 5,721 feet in Table 3. The nose fineness ratio, which is defined as nose Sustain range 12,712 20,197 feet length to body diameter, is reduced slightly due to the incre- Coast range 23,661 27,017 feet ment of diameter. However, the optimum nose length is reached at a baseline value. The optimum missile configuration shows a lower para- ðRangeÞi ðRangebaselineÞi site drag and higher lift to drag ratio values compared to

ðCDoÞi ðCDo baselineÞi the body-wing-tail configuration baseline for the boost, sustain, and coast missile flight conditions. It results in increas- ðC Þ ðC Þ L i L baseline i ing the range of boost, sustain and coast stage as shown in ðL=DÞi ðL=DBaselineÞi Table 3. The pitching and rolling moment coefficient constraints are satisfied while a bigger fin tail and further back ðjCljÞi ð0:3jClajÞi movement of tail location are made in the optimum missile ðjC jÞ ð0:3jC jÞ m i me i configuration as shown in Figs. 13 and 14. In addition, the Where: i ¼ boost, sustain, and coast center of gravity is moved backward 4 inches to satisfy Jul. 2014 N.-V. NGUYEN et al.: Investigations on Missile Configuration Aerodynamic Characteristics for Design Optimization 217

Optimum missile configuration Body-wing-tail configuration

Fig. 15. Air intercept missile mesh topology.

Fig. 13. 3D view of optimum conﬁguration comparison with a baseline body-wing-tail conﬁguration.

Fig. 16. Pressure coefficient contours along an optimum missile configu- Fig. 14. 2D view of optimum missile compared with a baseline body- ration. wing-tail configuration.

18 TMD analysis 16 pitching and rolling moment coefficient. ANSYS-Fluent 14 Missile DATCOM Therefore, the missile configuration design optimization 12 problem is successfully formulated to obtain an optimum 10 missile configuration with an improvement in total missile CN 8 range while implementing aerodynamics and stability data- 6 4 base generated from Missile DATCOM to replace aerody- 2 namics analysis module in the TMD Spreadsheet. 0 4.6. High-fidelity analysis validation 0 2 4 6 8 10 AoA (deg.) High-fidelity analysis ANSYS Fluent 1320) is used to validate the optimal configuration results as shown in Fig. 13. Fig. 17. Normal force validation for the optimum missile configuration. Steady state calculations are used to compute aerodynamic coefficients and flow field of the optimum missile configura- shown in Fig. 15. Due to the complex flow at the rear part tion using ANSYS Fluent 13. The mesh is modeled using of the missile it is decided to use a density-based solver with Pointwise 1622) grid generation software. Reynolds-aver- CFL number equal to 0.5 at the first 5,000 iterations and 3 aged Navier-Stokes (RANS) equations are applied to to 5 at later iterations. This approach allows us to obtain a describe flow around the missile. The single equation converged solution of the flow around the optimum missile Spalart-Allmaras turbulent model (S-A), which was specif- configuration. Convergence criteria is selected as the maxi- ically developed by Spalart and Allmaras for aerospace mum residual of velocity components, energy and continu- applications involving wall-bounded flows, is used in the ity less than 104. current calculation. The model shows good agreement for The pressure coefficient contours along the missile sur- boundary layers subject to adverse pressure gradients. face are shown in Fig. 16 for 5 degrees of AoA. The weak Flow around half of the optimum missile configuration is shock captured at the top surface of the wing and strong investigated due to symmetric missile geometry. For precise pressure gradient at missile nose area are observed. The calculation of boundary layer properties, dense mesh is gen- high-fidelity ANSYS Fluent 13 is calculated for 0, 5 and erated around missile configuration. Yþ value at the wing 10 degrees of AoA as shown in Fig. 16. The normal force and tail surface is equal to 1.0 and greater than 1.0 at the coefficient results on the missile optimum configuration body surface. Applying a Yþ value at the body surface of are also performed with the TMD Spreadsheet aerodynam- less than 1.0 leads to high aspect ratio cells and mesh geom- ics analysis model and missile DATCOM to compare with etry problems. Dense mesh with a number of grid points of the high-fidelity ANSYS Fluent 1320) analysis results in 3.1 million is used to precisely predict aerodynamic charac- Fig. 17. The comparison graph indicates that the TMD teristics of the optimum configuration. Grid topology is Spreadsheet and Missile DATCOM predict a normal force 218 Trans. Japan Soc. Aero. Space Sci. Vol. 57, No. 4

Table 4. Normal force results comparison with ANSYS Fluent 13. Acknowledgments AoA ANSYS- Missile Difference TMD Difference (degree) Fluent DATCOM (%) analysis (%) The authors would like to acknowledge that this research was supported by the Ministry of Education, Science and Technology 00 0 0 0 0 (MEST), Space Core Technology Development Program–a 5 4.57 4.82 5.49 5.19 13.52 grant number 2012033521 and the 2013 KU Brain Pool (Konkuk 10 8.07 9.56 11.76 11.13 37.95 University), and the corresponding author for the grant Jae Woo Lee.. coefficient quite close to high-fidelity analysis results at low References AoA of approximately 5 degrees. At higher AoA, the TMD Spreadsheet and Missile DATCOM shows an over- 1) Blake, W. B.: Missile DATCOM User’s Manual–1997, Fortran 90 estimated lift coefficient as shown in Fig. 17. The Missile Revision, 1998. 2) White, J. T.: An Assessment of Missile Datcom Prediction Accuracy DATCOM is closely predicted with ANSYS Fluent 13 Relative to Generic Body+Wing+Tail Missile Pitch Aerodynamics, results compared with TMD analysis as shown in Table 4. AIAA Paper 95-1893-CP, 1995. The maximum normal force coefficient difference with 3) Abney, E. J. and McDaniel, M. A.: High Angle of Attack Aerody- ANSYS Fluent 13 is 11.76% at 10 degrees of AoA while namic Predictions Using Missile Datcom, AIAA Paper 2005-5086, 2005. the TMD aerodynamics analysis result shows a 37.95% 4) Smith, E. H., Hebbar, S. K. and Platzer, M. R.: Aerodynamic Charac- difference with ANSYS Fluent at 10 degrees of AoA in teristics of a Canard-Controlled Missile at High Angles of Attack, Table 4. In addition, the designed missile mission profile J. Spacecraft Rockets, 31, 5 (1994), pp. 766–772. operates at approximately 7 degrees of AoA as shown in 5) Riddle, D. B., Hartfield, R. J., Burkhalter, J. E. and Jenkins, R. M.: Genetic-Algorithm Optimization of Liquid-Propellant Missile Sys- Fig. 12. Therefore, it is worthy to replace an aerodynamics tems, J. Spacecraft Rockets, 46, 1 (2009), pp. 151–159. analysis module in the TMD Spreadsheet by Missile 6) Riddle, D. B., Hartfield, R. J., Burkhalter, J. E. and Jenkins, R. M.: Ge- DATCOM for obtaining more accuracy and reliability at a netic Algorithm Optimization of Liquid Propellant Missile Systems, missile conceptual design stage. AIAA Paper 2007-362, 45th AIAA Aerospace Sciences Meeting and Exhibit, 2007. 7) Talpallikar, M. V. and Nelsont, H. F.: Modeling Supersonic Missile 5. Conclusion Fin-Body Interference for Preliminary Design, J. Spacecraft Rockets, 27, 6 (1990), pp. 571–576. The investigations on short and medium range missile 8) Zipfel, P. H.: Modeling and Simulation of Aerospace Vehicle Dynam- ics, 2nd ed., AIAA Education Series, 2007. aerodynamic characteristics of medium range configuration 9) Leng, G.: Compression of Aircraft Aerodynamic Database Using Mul- and short range configuration were addressed by implement- tivariable Chebyshev Polynomials, Adv. Eng. Software, 28, 2 (1997), ing the results from a developed Aero DB program. The val- pp. 133–141. idations of Missile DATCOM were reproduced for the 10) Chen, Y., Kopp, G. A. and Surry, D.: Interpolation of Pressure Time Series in an Aerodynamic Database for Low Buildings, J. Wind body-wing-tail configuration by comparing with experiment Eng. Ind. Aerodynam., 91, 6 (2003), pp. 737–765. data and AeroPrediction AP98. The investigations on 11) Min, B.-Y., Lee, J.-W. and Byun, Y.-H.: Numerical Investigation of medium and short range configuration aerodynamic coeffi- the Shock Interaction Effect on the Lateral Jet Controlled Missile, cients show the correct aerodynamics trend and capture Aerospace Sci. Technol., 10, 5 (2006), pp. 385–393. 12) Monta, W. J.: Supersonic Aerodynamic Characteristics of a Sparrow the physical phenomena of air-to-air missiles. III Type Missile Model with Wing Controls and Comparison with The conceptual missile design optimization process was Existing Tail-Control Results, NASA Technical Paper 1078, 1977. established to obtain a quick and relatively accurate optimal 13) Sooy, T. J. and Schmidt, R. Z.: Aerodynamic Predictions, Compari- missile configuration. The Aero DB was implemented suc- sons, and Validations Using Missile DATCOM (97) and Aeropredic- tion 98 (AP98), J. Spacecraft Rockets, 42, 2 (2005), pp. 257–265. cessfully and efficiently into a missile conceptual design 14) Raytheon Co., http://www.raytheon.com/ stage for replacing aerodynamic analysis module of the 15) Moore, F. G. and Moore, L. Y.: 2009 Version of the Aeroprediction TMD Spreadsheet and providing stability coefficient con- Code: AP09, J. Spacecraft Rockets, 45, 4 (2008), pp. 677–690. straints supporting resizing of an air-to-air missile configu- 16) Vulkelich, S. R., Stoy, S. L., Burns, K. A., Castillo, J. A. and Moore, M. E.: Missile DATCOM Volume I—Final Report, McDonnell Doug- ration by maximizing total range performance. A 27.8% las Missile Systems Co., 1988. improvement in a total range was obtained by an optimal 17) Jorgensen, L. H.: Prediction of Static Aerodynamic Characteristics for missile configuration while satisfying given aerodynamics, Slender Bodies Alone and with Lifting Surfaces to Very High Angles stability and performance constraints. of Attack, NASA TR-R-474, 1977. 18) Fleeman, E. L.: Tactical Missile Design, AIAA Education Series, The high-fidelity analysis performed on the optimal mis- 2001. sile configuration using ANSYS Fluent 13 demonstrated 19) ModelCenter 10.1, PHX ModelCenterÒ, http://www.phoenix-int.com/ more accurate and reliable results provided by Aero DB software/phx-modelcenter.php rather than the TMD Spreadsheet aerodynamics analysis at 20) ANSYS Fluent 13, ANSYS, Inc., www.ansys.com 21) Booker, A. J., Meckesheimer, M. and Torng, T.: Reliability Based angle of attack up to 10 degrees. Design Optimization Using Design Explorer, Optim. Eng., 5,2 (2004), pp. 179–205. 22) Pointwise 16 User Manual, http://www.pointwise.com/