. Asrecently as ﬁve to ten years ago, mesh generation was fre-quently the most time consuming task in a typical CFD cycle.Adaptive Cartesian mesh generation methods are capable ofproducing millions of cells around complex geometries inminutes and have substantially removed this bottleneck.Why write yet another Euler solver? With robust mesh gener-ation largely in-hand, solution time resurfaces as the pacingitem in the CFD cycle. The current work attacks this issue bydesigning a scalable, accurate Cartesian solver with robustmultigrid convergence acceleration. Our primary motivationis to gain efﬁciency by capitalizing on the simpliﬁcations andspecialized data structures available on Cartesian grids. Sig-niﬁcant savings in both CPU time and storage may be real-ized by taking advantage of the fact that cell faces arecoordinate aligned. In addition, higher-order methods withgood limiters are generally easier to design and perform morerobustly on uniform Cartesian meshes.Secondly, in any embedded-boundary Cartesian solver, thebody-intersectingcut-cellsdemand special attention. Thesecells can impose a substantial burden on the numerical dis-cretization since the arbitrary nature of geometric intersec-tion implies that a cut-cell may be orders of magnitudesmaller than its neighboring cells. This fact contrasts sharplywith the comparatively smooth meshes that are generallyfound on a good quality structured or unstructured mesh.Substantial research into these cut-cell issues have been stud-ied by references [9],[10],[6],[8], and [12] (among others)and we hope to take advantage of this investment.Thirdly, this work investigates a multigrid strategy that isspecialized for adaptively reﬁned Cartesian meshes. In ourapproach, all grids in the multigrid hierarchy cover the entiredomain and include cells at many reﬁnement levels. Thesmoother therefore iterates over the entire domain when it isinvoked on any grid in the hierarchy. In this respect, theapproach shares more with agglomeration or algebraic multi-grid techniques than with many other Cartesian or AMRmethods which iterate over only cells at the same level ofreﬁnement

A Parallel Multilevel Method for Adaptively Refined Cartesian Grids with Embedded Boundaries

This article presents a complete design concerning the guidance and autopilot modules for a class of spin-stabilized fin-controlled projectiles. The proposed concept is composed of two sections: the rapidly spinning aft part contains the charge, whereas the front part, which is roll decoupled from the aft, includes all the necessary electronic equipment and actuator devices needed for guidance and control. As far as the front section is concerned, a skid-to-turn control configuration is adopted, employing two pairs of movable trajectory correction aerodynamic surfaces, whereas a coaxial motor is added for nose roll angle positioning. The main advantage of the overall setup is that, on the one hand, it maintains the inherent dynamic stability properties of a rapidly spinning body due to the aft part, while at the same time, the front part, containing the guidance fuse, remains easy to be fit to any unguided projectile, hence transforming it into a guided one. The design of the guidance and control modules ...

Guidance and Control Design for a Class of Spin-Stabilized Fin-Controlled Projectiles

This article describes a new multidisciplinary computational study undertaken to compute the flight trajectories and simultaneously predict the unsteady free-flight aerodynamics of a finned projectile configuration. Actual flight trajectories are computed using an advanced coupled computational fluid dynamics/rigid body dynamics technique in a body-fixed coordinate system. An advanced time-accurate Navier–Stokes computational technique has been used in computational fluid dynamics to compute the unsteady aerodynamics associated with the free flight of the finned projectile at supersonic speeds. Computed positions and orientations of the projectile have been compared with actual data measured from free-flight tests and are found to be generally in good agreement with the data. Predicted aerodynamics forces and moments also compare well with the forces and moments used in the 6 degree of freedom fits of the results of the same tests. Unsteady numerical results obtained from the coupled method show the flowfield, the aerodynamic coefficients, and the flight paths of the projectile.

Time-Accurate Numerical Prediction of Free-Flight Aerodynamics of a Finned Projectile

: The prediction of the dynamic stability derivatives-roll-damping, Magnus, and pitch-damping moments-were evaluated for three spin-stabilized projectiles using steady-state computational fluid dynamic (CFD) calculations. Roll-damping CFD predictions were found to be very good across the Mach number range investigated. Magnus moment predictions were very good in the supersonic flight regime; however, the accuracy varied in the subsonic and transonic flight regime. The best Magnus moment prediction in the subsonic flight regime was for the square-base projectile that did not exhibit highly nonlinear Magnus moments. A primary contribution of this report is the demonstration that the pitch-damping moment can be adequately predicted via steady-state methods rather than resorting to unsteady techniques. The predicted pitch-damping moment compared very well to experimental data for the three projectiles investigated. For one configuration, the pitch-damping moment was predicted by several CFD codes, two different steady-state methods, and a time-accurate planar pitching motion method. All methods compared very well to each other and to the experimental data.

Navier-Stokes Predictions of Dynamic Stability Derivatives: Evaluation of Steady-State Methods

Instrumented flight experiments were conducted to quantify flight behavior for two precision munitions programs.These projectileswere of different shapes and calibers but each featured roll-inducing tailfins and canards as their maneuver mechanisms. In this effort, aerodynamic terms for asymmetries, side moments, and control mechanisms were estimated from onboard sensor data acquired during elevated gun firings. Additionally, these experiments uncovered an in-flight reversal in coning direction of the projectile and the reasons for this behavior are described in a flight stability analysis.

Experimental Flight Characterization of Asymmetric and Maneuvering Projectiles from Elevated Gun Firings

: Computational fluid dynamic simulations (CFD) were used to predict the aerodynamic coefficients and flow field over a spinstabilized, 25-mm, sub-caliber training projectile. The primary objective of the investigation was to determine the CFD parameters necessary for the accurate prediction of the Magnus moment and roll damping of a spin-stabilized projectile. Archival experimental data was used to validate the numerical calculations. The Mach number range investigated was from 0.4 to 4.5. Steady state CFD calculations predicted the drag, normal force, pitching moment, and normal force center of pressure very well to within 10% of the experimental data. Time-accurate, detached-eddy simulations were found necessary to predict the Magnus moment in the subsonic and transonic flow regimes. Steady state CFD was found adequate to calculate the roll damping, which was predicted to within 15% of the experimental data in both steady state and time accurate calculations.

CFD Computation of Magnus Moment and Roll Damping Moment of a Spinning Projectile

Precision-guided munitions are of interest to the Army as a means of both reducing collateral damage and increasing the chance of desired effect with the first round fired. Many technical barriers ...

/pdf/flight-mechanics-of-a-novel-guided-spin-stabilized-3w3x9c78wk.pdf

Flight Mechanics of a Novel Guided Spin-Stabilized Projectile Concept

The flow interaction effects from a jet issuing into a supersonic crossflow are investigated using computational fluid dynamic simulations of a basic fin-stabilized projectile at moderate positive and negative angles attack. Data was generated for a high-pressure ratio jet located at seven locations along the projectile axis. Crossflow Mach numbers of 1.5, 2.5, and 3.5 were investigated for an angle of attack range of -10° ≤ α ≤ 10°. Flowfield visualizations indicated the size of the jet plume and the size of the resulting low-pressure region behind the jet were reduced as Mach number increased. The jet force amplification factor showed more variation as α became more negative. The effective jet location was found to vary little for α > -5° at Mach 2.5 and 3.5. For α > -5°, there was less variation of force amplification factor a Mach number increased. Flight simulations using reaction jet “squibs” were performed to evaluate the sensitivity of the control maneuver to the differences in jet thrust and jet actuation location. These results showed that significant differences in the projectile maneuver control were obtained if the effective jet thrust acting at the effective jet location were used instead of the ideal jet thrust acting at the jet exit location.

Lateral Jet Interaction on a Finned Projectile in Supersonic Flow

Viscous computational fluid dynamic simulations were used to predict the aerodynamic coefficients and flowfield around a generic canard-controlled missile configuration in supersonic flow. Computations were performed at Mach 1.5 and 3.0, six angles of attack between 0 and 10 deg, with 0- and 10-deg canard deflection, and with planar and grid tail fins, for a total of 48 cases. Validation of the computed results was demonstrated by the very good agreement between the computed aerodynamic coefficients and those obtained from wind-tunnel measurements. Visualizations of the flowfield showed that the downwash off of the canards produced a low-pressure region on the starboard side of the missile that, in turn, produced an adverse side force. The pressure differential on the leeward fin produced by the interaction with the canard trailing vortices is primarily responsible for the adverse roll effect observed when planar fins are used. Grid tail fins improved the roll effectiveness of the canards at low supersonic speed. Flow visualizations from the simulations performed in this study help in the understanding of the flow physics and can lead to improved canard and tail fin designs for missiles and rockets.

James DeSpirito

Papers

CFD Computation of Magnus Moment and Roll Damping Moment of a Spinning Projectile

Navier-Stokes Predictions of Dynamic Stability Derivatives: Evaluation of Steady-State Methods

Flight Mechanics of a Novel Guided Spin-Stabilized Projectile Concept

Lateral Jet Interaction on a Finned Projectile in Supersonic Flow

Numerical Investigation of Canard-Controlled Missile with Planar and Grid Fins