A study of unsteady projectile aerodynamics using a moving coordinate method
01 May 2007-Vol. 221, Iss: 5, pp 691-706
TL;DR: In this paper, a computational fluid dynamics (CFD) method has been applied to simulate unsteady near-field aerodynamics of the projectile which is launched from a ballistic range.
Abstract: A computational fluid dynamics (CFD) method has been applied to simulate unsteady near-field aerodynamics of the projectile which is launched from a ballistic range. A moving coordinate scheme for a multi-domain technique was employed to investigate the unsteady flow with moving boundary. The coordinate system fixed to each moving domain was applied to the multi-domains, and the effect of virtual mass was added in the governing equations for each domain. The unsteady, axi-symmetric Euler equation systems were numerically solved using the third-order Chakravarthy-Osher total variation diminishing scheme, with Monotone Upstream-centered Scheme for Conservation Laws (MUSCL) approach. The present computations were validated with results of some other CFD works and experimental data available. The computed results reasonably capture the major flow features, such as shock waves, blast waves, shear layers, vortical flows, etc which are generated in launching a projectile up to a supersonic speed. The pro...
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TL;DR: In this article, a computational study using a moving grid method is performed to analyze various fluid dynamic phenomena in the near field of a gun, such as the projectile-shock wave interactions and interactions between the flow structures and the aerodynamic characteristics of the projectile when it passes through various flow interfaces.
Abstract: The aerodynamics of projectiles launched from barrels of various devices is quite complicated due to their interactions with the unsteady flowfield around them. A computational study using a moving grid method is performed here to analyze various fluid dynamic phenomena in the near field of a gun, such as the projectile–shock wave interactions and interactions between the flow structures and the aerodynamic characteristics of the projectile when it passes through various flow interfaces. Cylindrical and conical projectiles have been employed to study such interactions and the fluid dynamics of the flowfields. The aerodynamic characteristics of the projectile are hardly affected by the projectile configuration during the process of the projectile overtaking the primary blast wave for small Mach numbers. However, it is noticed that the projectile configurations do affect the unsteady flow structures before overtaking and hence, the unsteady drag coefficient for the conical projectile shows considerable vari...
12 citations
01 Mar 2019
TL;DR: Comparisons indicate that the round nose projectile had the best performance at long distances compared to the other samples, while the flat nose projectile exhibited great performance at short distances, but behaved weakly at long distance.
Abstract: Shooting accuracy of air gun projectiles is very important in sport tournaments and has always been questioned by enthusiasts. For this purpose, the performance of four samples of air gun projectil...
10 citations
Cites methods from "A study of unsteady projectile aero..."
...The time-stepping approach can be written as shown in equation (11)...
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...The flow equations shown in equation (11) are solved using Jameson’s four-stage scheme(17) and with the equations of the projectiles’ motion and the turbulence equations k–kL–v in simultaneous and coupled form using a moving computational grid....
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TL;DR: In this article, the effects of the projectile overtaking amoving shock wave on the projectile aerodynamic characteristics were analyzed using a moving-grid method to analyze the effect of the collision on the aerodynamic properties.
Abstract: A projectile that passes through a moving shock wave experiences drastic changes in the aerodynamic forces as it moves from a high-pressure region to a low-pressure region. These sudden changes in the forces are attributed to the wave structures produced by the projectile–shock-wave interaction and are responsible for destabilizing the trajectory of the projectile, consequently leading to a loss of projectile stability and control efficiency. A computational study was performed here using a moving-grid method to analyze the effects of the projectile overtaking amoving shock wave on the projectile aerodynamic characteristics. A one-dimensional analysis was also carried out to identify the projectile overtaking criteria. The analytical results show that the projectile overtaking flowfields canbe in a subsonic or supersonicflowregime, based on the relative projectileMachnumber.However, it is found that the actual flowfields in the present computations cannot be distinguishedwith the relative projectileMach number only, because theblast-wave strength is diminishingwith time and space. The aerodynamic characteristics of the projectile are hardly affected by the overtaking process for smaller blast-waveMach numbers, as the blast wave will become weak by the time it is overtaken by the projectile. The projectile drag coefficient is more greatly affected by the unsteady flow structures through which the projectile travels in the near field than by the overtaking process.
10 citations
TL;DR: In this article, a numerical study of the shocked flows generated by a supersonic projectile released from a launch tube into a big chamber has been performed based on fixed Cartesian grids, the two-dimensional axisymmetric Euler equations are solved by the fifth-order WENO scheme implemented with moving boundary conditions.
Abstract: Numerical study of the shocked flows generated by a supersonic projectile released from a launch tube into a big chamber has been performed in this paper. Based on fixed Cartesian grids, the two-dimensional axisymmetric Euler equations are solved by the fifth-order WENO scheme implemented with moving boundary conditions. Both the level set technique and ghost fluid method are used for capturing the moving interface of the projectile implicitly. The numerical results show that complex shock phenomena exist in the transient shock flow, resulting from shock-wave reflection, shock-wave focusing, shock-wave/projectile interaction and shock-wave/contact surface interactions. The relationships between the acceleration of the projectile and the transient shock flow are also discussed in detail.
9 citations
TL;DR: The implemented experimental high-speed BOS setup has demonstrated its ability to capture clearly the salient features of the precursor and the propellant gas flow fields and their interactions, confirming the BOS capability to visualize complex density flow fields.
Abstract: Several experimental and numerical studies on muzzle blast and flow fields have been performed. However, due to the extremely short duration and the spatiotemporal evolution of these flows, experimental quantitative techniques are limited. As a consequence, the number of validated numerical calculations is limited as well. On the other hand, despite the development of computer models that have succeeded in predicting the measured pressure and velocity, they show unrealistic temperatures and densities. Therefore, temperature and/or density measurements are required to validate these codes, thus the motivation of this research. The present paper focuses on the development of a density-sensitive and non-intrusive measurement technique and the implementation of a quantitative flow visualization method based on Background-Oriented Schlieren (BOS) combined with a high-speed camera. In BOS, the experimental setup of conventional Schlieren (mirrors, lenses, and knife-edge) is replaced by a background pattern and a single digital camera. The muzzle flow fields and the flow field around a 5.56-mm projectile in flight were successfully visualized. Indeed, the implemented experimental high-speed BOS setup has demonstrated its ability to capture clearly the salient features of the precursor and the propellant gas flow fields and their interactions. The captured structures such as vortex, barrel shock, Mach disk, and blast wave show a good agreement with that issued from a realized conventional Schlieren setup and the bibliography, confirming the BOS capability to visualize complex density flow fields.
9 citations
References
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TL;DR: In this article, a coordinate-free formulation of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system, and the analysis considers general types of equations: potential, Euler, and Navier-Stokes.
Abstract: Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations: potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomenclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.
324 citations
TL;DR: In this paper, the axisymmetric Navier-Stokes equations are solved on a fine grid, and the grid convergence of the drag coefficient is achieved, which is validated by comparing the experimental data of a 80 mm sphere, measured by the accelerometer in a vertical shock tube.
Abstract: The dynamic drag coefficient of a sphere by shock wave loading is investigated numerically and experimentally. The diameter of the sphere is varied from 8 \({\mathrm{\mu}}\)m to 80 mm in numerical simulation. The axisymmetric Navier-Stokes equations are solved on a fine grid, and the grid convergence of the drag coefficient is achieved. The numerical result is validated by comparing the experimental data of a 80 mm sphere, measured by the accelerometer in a vertical shock tube. It is found that the sphere experiences in the early interaction one order higher drag than in the steady state. A transient negative drag, mainly resulting from the focusing of shock wave on the rear side of the sphere, is observed only for high Reynolds number flows, and the drag becomes positive because of increased skin friction for low Reynolds number flows.
113 citations
TL;DR: In this paper, the structure of the flowfields formed about the muzzle of a small caliber rifle during the firing were measured using a time-resolved, spark shadow-graph technique. But the results were limited.
Abstract: The structure of the flowfields formed about the muzzle of a small caliber rifle during the firing are measured using a time-resolved, spark shadow-graph technique. The initial flow from the muzzle occurs as tube gases are forced out ahead of the projectile. The gas is air and the exit properties are Ve =945 m/sec, Me = 1.48 and Pel POO = 15. A second flowfield forms upon separation of the projectile which releases the propellant gases. After an initial, in-bore expansion, the propellant gas muzzle properties are Ve=\29S m/sec, Afe = 1.0, and Pe/Poo =600. While the exit properties are different, the flowfields develop in a similar manner. In the axial or downrange direction, strong coupling between the jet and blast fields is observed; however, along the lateral boundaries, the coupling is very weak with the jet structure remaining invariant once established. Motion of observable discontinuities along the axis of symmetry is shown to qualitatively agree with variable energy blast wave theory. At late times, the air blast and jet flows are shown to uncouple and decay independently.
84 citations
TL;DR: In this paper, a numerical study of the interaction of plane blast waves with a cylinder is presented, which reveals that the blast-wave duration significantly influences the unsteady flow over the cylinder.
Abstract: A numerical study of the interaction of plane blast waves with a cylinder is presented. Computations are carried out for various blast-wave durations and comparisons are obtained with the corresponding results of planar shock-wave. Both inviscid and viscous results based on the solution of the Euler and Navier-Stokes equations are presented. The equations are solved by an adaptive-grid method and a second-order Godunov scheme. The shock wave diffraction over the cylinder is investigated by means of various contour plots, as well as, pressure and skin-friction histories. The study reveals that the blast-wave duration significantly influences the unsteady flow over the cylinder. The differences between the viscous and inviscid results are also discussed.
66 citations
TL;DR: In this article, the performance of seven high-resolution schemes is investigated in various unsteady, inviscid, compressible flows, and the results reveal that the Roe, HLLC and hybrid TVD schemes provide similar and overall the best results.
Abstract: The performance of seven high-resolution schemes is investigated in various unsteady, inviscid, compressible flows. We employ the Roe, HLL (Harten, Lax and van Leer), and HLLC (Toro et al.) Riemann solvers, two variants of the van Leer and Steger–Warming flux vector splitting (FVS) schemes, Rusanov's scheme, and a hybrid total variation diminishing (TVD) scheme that combines a high-order Riemann solver with a flux vector splitting scheme. The above schemes have been implemented in conjunction with an implicit-unfactored method which is based on Newton-type sub-iterations and Gauss–Seidel relaxation. The performance of the schemes has been assessed in six unsteady flow problems: two one-dimensional shock tube problems, shock-wave reflection from a wedge, shock-wave diffraction around a cylinder, blast-wave propagation in an enclosure, and interaction of a shock wave with a gas bubble. More dissipative schemes do not necessarily provide faster convergence per time step and also suppress instabilities that occur in certain unsteady flow problems. The efficiency of the solution depends strongly on the advective (high-resolution) scheme. The results reveal that the Roe, HLLC and hybrid TVD schemes provide similar and overall the best results. For the unsteady problems considered here, the computations show that an explicit implementation based on a TVD, fourth-order Runge–Kutta method results in longer computing times than the implicit-unfactored method.
60 citations