By adopting the irrotational and steady motion of the ideal compressible fluid and the supercavity with the Riabushinsky scheme of closure, an integro-differential equation was derived for the supercavitating flow around a slender cone-shaped projectile traveling in water at supersonic speed by using the slender-body theory and the matched-asymptotic-expansions method. The second-order approximation solutions for the supercavity profiles considering the compressibility effect were obtained,and the calculation precision was improved. The influences of the fluid compressibility on the supercavity profiles were analyzed under the high-speed impact of the gun-launched projectile. The fluid compressibility causes slight asymmetry of the supercavity profile, in which the forward part is narrower than the backward part. Because of the compressibility effect, when 1＜(Ma)∞＜（2）, the supercavity profile will expand similarly to the subsonic case; the supercavity profile will keep unchangeable when (Ma)∞ =（2）; and the supercavity profile will occur to a whole contraction when (Ma)∞＞（2）.%采用理想可压缩流体无旋定常流动以及超空泡尾部Riabushinsky闭合方式假定,基于细长体理论和匹配渐近展开法,建立了描述水下超声速条件下细长锥型射弹超空泡流动的积分微分方程.求解得到了考虑压缩性影响的超空泡形态二阶近似解,改进了超空泡形态的计算精度.分析了超声速射弹高速冲击条件下流体压缩性对超空泡形态的影响.流体压缩性导致超空泡形态前后稍微不对称,前端比尾端截面更窄.当1<(Ma)∞<√2时,流体压缩性效应对超空泡的影响与亚声速情况类似,使超空泡形态发生整体膨胀变化.当(Ma)∞=√2时,流体压缩性对超空泡形态无影响.直到(Ma)∞>√2以后,流体压缩性使超空泡形态发生反向改变,呈现整体收缩变化.
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