Numerical Prediction of Roll Damping and Magnus Dynamic Derivatives for Finned Projectiles at Angle of Attack

Abstract

The roll damping and Magnus dynamic derivatives, as well as total aerodynamic coefficients, were numerically predicted for two basic fin-stabilized projectiles at a supersonic Mach number of 2.49 for angles of attack ranging from -5 to 90 degrees. The aerodynamic coefficients were computed via time-accurate Reynolds-averaged Navier Stokes numerical methods, and were compared with archival wind tunnel data. Fair to excellent comparisons with experiment were obtained for the total and dynamic coefficients for the full angle of attack range, except for axial force which was overpredicted. Numerical modeling parameter studies were conducted to include dependence on spin rate, grid resolution, temporal resolution and other numerical convergence parameters. Nomenclature & Abbreviationsroll damping moment coefficient = Magnus force spin derivative coefficient = Magnus moment spin derivative coefficient = Magnus force derivative coefficient = Magnus moment derivative coefficient = pitch plane angle of attack, degrees or radians = spin rate/roll rate, rad/s , p′ = non-dimensional roll rate = = roll angle, degrees or radians = roll frequency, Hz = time, s = transient physical/global timestep, s = global iterations per rotation cycle M = freestream Mach number = freestream velocity, m/s D = projectile base diameter = 1 caliber, m = reference surface area = , m 2 = freestream density, kg/m 3 1 Aerospace Engineer, WMRD Flight Sciences Branch, vishal.a.bhagwandin.civ@mail.mil. AIAA Member. 2 P 0 = total pressure, Pa T 0 = total temperature, K Re d = Reynolds number, based on projectile diameter k = turbulent kinetic energy, m 2 /s 2 ε = turbulent dissipation rate, m 2 /s 3 y + = non-dimensional wall distance aoa = angle of attack rad = radians ANF = Army-Navy Basic Finner AFF = Air Force Modified Basic Finner CFD = computational fluid dynamics RANS = Reynolds-averaged Navier-Stokes

Canards interference on the Magnus effect of a fin-stabilized spinning missile

“…During the unsteady calculation, the inner iteration step was set to 20. 16 To ensure the reliability of the numerical results, grid independence study was carried out, and the results from two turbulence models were compared, including the k − ω turbulence model and the γ − R e θ t transition model. 17–19…”

Application of harmonic balance method to aerodynamic characteristics prediction of spinning vehicle

“…A first-order implicit scheme is adopted for the time integration of the dual-time method. The physical timestep is set as 3 ϫ 10 Ϫ5 s. The number of inner iterations is set to 20 as suggested by previous study (Bhagwandin, 2012). The Spalart-Allmaras (S-A) model with a blended wall function is used to simulate the turbulence for both the HBM and the dual-time method (Spalart and Allmaras, 1992).…”

“…However, the flow over the spinning vehicle is complex; thus, the computational efficiency and accuracy restrict the application of CFD. Traditionally, the simulation of finned spinning vehicle is considered as an unsteady problem and is usually solved by the dual-time method which is designed for solving transient flow problems (Jameson, 1991;Bhagwandin, 2012). Dual-time method significantly reduces the influence of physics time steps on the numerical stability by introducing the pseudo-time step (DeRango and Zingg, 1997).…”

Body-fin interference on the Magnus effect of spinning projectile in supersonic flows

“…R-square describes the correlation between the response values and the predicted response values, and is defined as the ratio of the sum of squares of the regression and the sum of squares about the mean. The value of R-square is between 0 and 1, with values closer to 1 indicating better fits (Bhagwandin, 2012). The R-square values at angles of attack are bigger than 0.995, indicating that the curve fitting is accurate.…”

“…Three physical time steps were set to T 1 = 5 × 10 −5 s, T 2 = 1 × 10 −5 s, and T 3 = 5 × 10 −6 s, and the corresponding spin angles were 1.839°, 0.368°, and 0.184°. The inner iteration step was set to 20 (Bhagwandin, 2012). Figure 3 shows the aerodynamic coefficients obtained within a spin cycle using different time steps.…”