Nonlinear Aeroprediction Methodology for Roll Position of 45 Degrees

An Euler code is used to predict hypersonic missile ow elds and to determine the carryover factors for the effect of the body on wing lift K W ( (B) ) and for the effect of the wing on body lift K B( (W ) ). Results are presented for Mach 4, 6, 8, and 10 at an angle of attack of 2 deg. The missile has a conical nose, a cylindrical fuselage with a 1-deg are angle, and delta ns. Both £ and + n con gurationsare considered. Results are given for 20-and 30-deg semivertex angles as a function of nspan to body radius (at n leading edge), S/R LE . The wing-body carryover for £ ns is smaller for the top set of ns than it is for the bottom set of ns. The value of K W ( (B) ) for the missile with £ ns is slightly larger than it is for + ns at Mach 8 and 10. At Mach 4 and 6, K W ( (B) ) is independent of n con guration. K B( (W ) ) is larger for £ ns than it is for + ns, and it increases as semivertex angle decreases from 30 to 20 deg. K B( (W ) ) generally decreases as both Mach number and nspan increase. Equations and tables are presented for the carryover factors. Nomenclature A F = planform area of one n (A W =2), m 2 A R = aspect ratio of wing formed by joining two ns at their root chord A W = wing-planform area formed by two ns joined at their root chord, m 2 C L = lift coef cient referenced to A W C L B = lift coef cient, body alone C L B;® = lift curve slope, body alone C L M = lift coef cient, entire missile C L W = lift coef cient, wing alone C L W ;® = lift curve slope, wing alone F N ;i = normal force on i th n, N K B.W / = body-n carryover K F .B/;i = n-body carryover on i th n K W .B/ = wing-body carryover K B W .B/ = wing-body carryover ( ns 3 plus 4) K T W .B/ = wing-body carryover ( ns 1 plus 2) L B = lift, body alone, N L B.W / = body lift in presence of ns, N L F.B/;i = lift of i th n in presence of body, N L M = lift, entire missile, N L W = wing-alone lift (2 D 0), N M 1 = freestream Mach number P = pressure/(freestream pressure) q 1 = freestream dynamic pressure, N/m 2 R = body radius at end of nosecone, m R LE = body radius at root chord leading edge (1.419R), m S = nspan, from body centerline, m Z = missile axial distance, from nose, m Z LE = root-chord leading edge position, m ® eq = equivalent angle of attack, deg ® F = n angle of attack, deg ® 1 = missile angle of attack, deg ² = n semivertex angle (20, 30 deg) 2 = n angular position (0, 45 deg) µ f = body are angle (1 deg) Á = body angular position, deg (0 at top)

“…At high ® 1 , the data given in Ref. 2 show that C ns produce more lift than £ ns; consequently, the effects of roll angle on lift are in uenced by ® 1 .…”

Section: Resultsmentioning

confidence: 92%

Roll Effects on Carryover for Hypersonic Delta Fin Missiles

Nelson

2001

“…(9), whereas in Ref. 11, the cos (U ) term was to the rst power. The reason for the square is the fact that the cos (U ) term does two things.…”

Section: Wing-alone Modi Cationsmentioning

confidence: 98%

“…11 to account for the difference in load on the windward and leeward planes. This shift is added to Eq.…”

Section: Wing-alone Modi Cationsmentioning

confidence: 99%

Evaluation and Improvements to the Aeroprediction Code Based on Recent Test Data

Moore

McInville

Hymer

2000

Self Cite

The 1998 (AP98) and prior versions of the U.S. Naval Surface Warfare Center, Dahlgren Division Aeroprediction Code are based primarily on slender body and perturbation theories at low angle of attack and empirical constants that represent the nonlinear aerodynamics as a function of angle of attack, Mach number, aspect and taper ratio, and other missile geometric parameters. The primary database on which these empirical nonlinear constants were derived was based on the NASA/Tri-Service component database taken in the 1970s. This database was limited in body radius to wing semispan plus body radius ratios of 0.5. A more recent database taken by NASA and the former McDonnell Douglas Corporation investigated other values of the parameter: body radius to wing semispan plus body radius ratio of 0.25, 0.33, and 0.5. As a result of this new database, the empirical constants in the AP98 that represent many of the aerodynamic nonlinearities were ne tuned. This ne tuning, along with other minor improvements, has shown the average normal force coef cient errors to be reduced by anywhere from 10 to over 40% on various missile con gurations. The largest reductions in error were for con gurations where the AP98 average accuracy was the worst. These new improved empirical constants will be a part of the next planned release of the aeroprediction code in 2002 (AP02). The AP98 average error on normal force coef cient of § 10% will, therefore, be somewhat better for the AP02. Nomenclature A= planform area of wing in cross ow plane, ft 2 A P = planform area of body in cross ow plane, ft 2 A R = aspect ratio, b 2 / A W A ref = reference area (maximum cross-sectional area of body, if a body is present, or planform area of wing, if wing alone), ft 2 b = wing span (not including body), ft C A = axial force coef cient C dc = cross ow drag coef cient C M = pitching moment coef cient (based on reference area and body diameter, if body present, or mean aerodynamic chord, if wing alone; can be about nose or center of gravity location) C MB = pitching moment coef cient of body alone C N = normal force coef cient C NB = normal force coef cient of body alone C N B(V ) = negative afterbody normal-force coef cient due to canard or wing-shed vortices C NL = linear component of normal-force coef cient C NNL = nonlinear component of normal-force coef cient C N T (V ) = negative normal-force coef cient component on tail due to wing or canard-shed vortex C NW = normal force coef cient of wing alone C Na = normal-force coef cient derivative (C Na ) W , = normal-force coef cient slope of wing (C Na ) T and tail, respectively

Aerodynamic Characterization of a Generic High-Speed Projectile Configuration

Pokela,

Kumar,

Vasile

et al. 2024

A combined experimental and numerical study was conducted on a generic projectile configuration with low-aspect-ratio fins. The main objectives of this study were to characterize the aerodynamic behavior and validate numerical simulations for a range of Mach numbers (0.4–4) to facilitate an understanding of major flow features such as forebody and fin-generated shock waves, crossflow shear layer vortex, and fin vortex interactions. Measurements included forces and moments, surface oil flow visualization, and high-speed shadowgraph imaging. Numerical simulations were performed using the CFD++ solver. The results showed an excellent match between the experimental and numerical force and moment data. Pressure contours obtained using numerical simulations were integrated to obtain the contributions of individual components toward the total normal force on the body. Flow visualization results show a few complex and interesting flow features, such as shear layer roll-up, crossflow and fin tip vortex interactions, and shock-wave–boundary-layer interactions. The effects of vortex strength and location were analyzed to determine their contributions to the overall forces on the model. The database generated will be very useful for further validation of the numerical tool and a better understanding of vortex-dominated supersonic flows.