TY - JOUR
T1 - Hypersonic Limit for Steady Compressible Euler Flows Passing Straight Cones
AU - Li , Qianfeng
AU - Qu , Aifang
AU - Su , Xueying
AU - Yuan , Hairong
JO - Communications in Mathematical Analysis and Applications
VL - 2
SP - 136
EP - 167
PY - 2024
DA - 2024/07
SN - 3
DO - http://doi.org/10.4208/cmaa.2024-0008
UR - https://global-sci.org/intro/article_detail/cmaa/23226.html
KW - Compressible Euler equations, shock wave, conical flow, hypersonic limit,
Radon measure solution.
AB - <p style="text-align: justify;">We investigate the hypersonic limit for steady, uniform, and compressible polytropic gas passing a symmetric straight cone. By considering
Radon measure solutions, we show that as the Mach number of the upstream
flow tends to infinity, the measures associated with the weak entropy solution
containing an attached shock ahead of the cone converge vaguely to the measures associated with a Radon measure solution to the conical hypersonic-limit
flow. This justifies the Newtonian sine-squared pressure law for cones in hypersonic aerodynamics. For Chaplygin gas, assuming that the Mach number
of the incoming flow is less than a finite critical value, we demonstrate that
the vertex angle of the leading shock is independent of the conical body’s vertex angle and is totally determined by the incoming flow’s Mach number. If
the Mach number exceeds the critical value, we explicitly construct a Radon
measure solution with a concentration boundary layer.</p>