Effects of gravity and compressibility on supercavitating flowcaused by high speed projectile
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摘要: 超空泡射弹是一种新型的水下高速动能武器。基于理想可压缩势流理论，考虑流体的重力效应，建立了水下细长锥形射弹超空泡流动的统一理论模型和数值计算方法，分别导出了亚、超声速条件下用于计算细长锥形射弹超空泡形态的积分-微分方程。采用二次多项式局部拟合空泡，提出了超空泡形态的数值离散和递推求解方法。通过超空泡长细比的渐近解与数值解计算结果比较，验证了所建立的理论模型和计算方法的有效性。通过分析细长锥形射弹在不同运动方式、深度、速度条件下的超空泡形态和流体动力系数计算结果，明确了流体重力和压缩性效应对超空泡尺度、射弹表面压力分布和压差阻力系数的影响。Abstract: The supercavitating projectile is a new underwater weapon with high speed and kinetic energy. Based on the theory of the ideal compressible potential flow, and taking into account of the gravity effect, an unified theoretical model and numerical calculation for the supercavitating flow caused by an underwater slender conical projectile were constructed, the integral-differential equations for computing the supercavity profiles at subsonic and supersonic speed were derived, and the numerical discrete scheme and a recursive solution were proposed using local fitting of quadratic polynomial, thus obtaining the supercavity profile. The theoretical model and numerical calculation were verified by comparing the asymptotic solutions with the numerical ones of the supercavity aspect ratio. The effects of gravity and compressibility on the supercavity scale, pressure distribution over the projectile and base drag coefficient were summarized through analysis of the supercavity profiles and hydrodynamic coefficients in different movement modes, depths and speeds for the slender conical projectile.
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Key words:
- fluid mechanics /
- compressibility /
- potential flow theory /
- supercavity /
- projectile /
- subsonic /
- supersonic /
- gravity
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图 1 细长锥形射弹及超空泡坐标系
Figure 1. Coordinate system on slender conical projectile and supercavity
图 2 超空泡长细比的数值解与渐近解
Figure 2. Supercavity aspect ratio between numericaland asymptotic solution
图 4 出水与水平运动超空泡长度和最大半径之比
Figure 4. Ratio of supercavity length to maximum radiusfor upward to horizontal movement
图 8 不同深度时压差阻力系数与马赫数的关系
Figure 8. Base drag coefficient vs. Mach numberat different depths
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