Investigation of high-speed flow past a sphere in open and confined spaces*

High-speed motion of an object in a confined space induces compressible flow phenomena that are distinctly different from those in an open space. Axisymmetric Reynolds-averaged Navier-Stokes (RANS) equations were solved for the compressible flow past a sphere in both open and confined spaces. The Reynolds numbers considered range from 15,000 to 150,000, based on the sphere diameter. Additionally, the Mach numbers vary from 0.4 to 4, demonstrating various compressible flow phenomena around the sphere. For confined spaces, the considered blockage ratios (BR) were 0.09 and 0.4. A detached shock wave forms ahead of the sphere in open space when an object moves at a Mach number exceeding 1. However, in confined spaces, a compression region is generated below the Kantrowitz limit Mach number. Consequently, the drag coefficient in open and confined spaces exhibits different characteristics. To predict the bow shock wave profile and reflection location at a pipe wall, an analytical model combining theoretical considerations for the shock standoff distance and empirical relations for the wave shape was formulated. The drag coefficient in a low BR becomes identical to that in open space beyond a specific Mach number. In confined spaces, low and high BRs exhibit two distinct trends in drag coefficients. These findings on the new limit and drag coefficient enhance the understanding of compressible flow physics and aerodynamic characteristics at high Mach numbers in confined spaces.