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한국항공대학교 항공 모빌리티 및 공력음향학 연구실
Summary
Muzzle blast wave
A muzzle blast involves complex flow physics with a discontinuity nature in the flow field, which requires sophisticated numerical techniques and analysis for the understanding of the flow phenomena. The blast waves from a muzzle expand rapidly to the open flow region, and it evolves into various types of shock and vortex which generate noise sources. There are several previous studies that examined the mechanism of blast waves, which observed only a flow field or sound wave propagation without the projectile. However, for a more realistic approach and intuitive observation, the projectile supersonically released from a muzzle should be considered, since flow structures could be characterized by a movement of the projectile as well as blast wave itself. Moreover, studies on shock-vortex interaction and noise generation by moving bodies are of great interest in aerospace science and engineering fields especially regarding the analysis of launch vehicles or missiles.
Immersed boundary method (IBM)
One of the most efficient and widely used methods to capture this feature of fluid-solid interaction is Immersed Boundary Method (IBM) which can be characterized by its simple nature in dealing with a complex moving body. Among many possible variations of IBM, we focused on a “sharp-interface” type method that can achieve a higher order of accuracy. However, there are two drawbacks in using the sharp-interface method: First, numerical discretization near the immersed boundary experiences jump discontinuity which yields spurious waves. Even if this problem has been conventionally resolved by jump-correction in incompressible flow simulations, there is still a question about the implementation of jump-correction IBM to compressible flow. Second, the ghost point is susceptible to singularity, especially in moving body conditions. Therefore, in this paper, an optimized IBM is presented, in which continuity is defined and discontinuity by singularity could be avoided in the compressible flow simulation.
Objective & Contribution
Mathematical derivation and implementation of the optimized IBM
Analysis of complex flow field by blast waves around a projectile
Understanding of sound generation mechanism with a projectile by shock-vortex interaction
[Sound waves from muzzle blast]
Method
Shock tube-supersonic projectile problem
From observation of numerical and experimental researches, there are major three stages of the muzzle blast phenomena with a supersonic projectile. The precursor step is the first stage where the precursor shock wave develops (first blast wave) by the initial air which is propelled out of the muzzle ahead of the projectile. This shock wave is called the first blast wave. Contact discontinuity of the precursor shock wave disturbs the quiescent state and spherically propagates.
After all the initial gas is driven out, the projectile gets ejected out by the propellant gas, which is the discharge step. In this stage, the Prandtl-Meyer expansion fan occurs at the muzzle exit by propellant gas following behind the projectile. This expansion wave propagating into the pre-disturbed region is called a secondary blast wave.
The final stage is the disturbance step because the flow field becomes completely disturbed as the projectile breaks through the Mach disk with its own inertia. Highly coupled interaction between the projectile and surrounding flow field brings about bow shock, vortex, and shear layer, which inevitably generate acoustic sources. This type of fluid-solid interaction can be assumed one-way since the inertia of supersonic projectile within a short time surmounts drag forces. This flow physics and noise generation mechanism of muzzle blast with respect to the shapes of a supersonic projectile will be addressed. Taking advantage of the immersed boundary from which the complex shape of projectiles could be utilized with no additional cost.
[Schematic design of computational domain]
[Blast wave ejection from shock tube]
Results
Sound generation process
From Helmholtz decomposition, it is found that sound is generated where shocklet and vortex collides which brings about shock-vortex interaction. There are representative five sound sources, and 1st and 4th sound sources induce major sound waves.
Forward Vortex Ring from the projectile head by K-H instability affects the sonic boom (1st sound source) interacting with shock waves. It merges with projectile-induced waves to a sonic boom. This sound wave shows dominant features of propagating in firing direction (no effects on upstream).
In this problem, 4th sound source is determined by interactions of VIS (Vortex Induced Shock) and FVR (Forward Vortex Ring), which are maximized when FVR moves toward VIS in the normal direction. This sound wave propagates upstream with several wavelets, and it shows non-linear strong waves depending on vortex strength. The impinging angle of the highly vortical region and shock waves affects the sound generation.
[Sound generation process of muzzle blast wave ]
(PVR: Primary vortex ring | VIS: Vortex induced shock | FVR: Forward vortex ring | DSW: Diffracted shock wave)
Conclusion
The optimized immersed boundary method is developed for compressible flow and the algorithm is mathematically derived. Through the acoustic scattering problem, it has been shown that the field reconstruction with jump-correction allows continuous discretization across the immersed boundary so that the solution could use weak or no damping near the immersed boundary, which makes it more physically reasonable and numerically stable. The present method is implemented in order to perform a numerical study on the muzzle blast wave problems. With the stable shock-capturing method, the evolution of flow structures is calculated and analyzed in detail. It is found that vortical structures from the interaction of the second vortex ring and bow shock generate complex flow fields called the vortical interaction area. In order to figure out the noise generation mechanism more clearly, the Helmholtz decomposition and acoustic perturbation equations are used. Lamb vector and velocity gradient indicated that this noise source is generated from the vortical interaction region which is induced by shock-vortex interaction. It is found that the shapes of the projectiles are an important factor to determine the noise source. Sharper projectiles tend to produce stronger noise sources in the radial direction as bow shock interacts with the 2nd vortex ring in earlier times where the vortex strength remains more intensive.
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