Why is critical Mach number of a sphere higher than a cylinder ?
Critical Mach number is the free stream Mach number, such that local Mach number on the surface of the body is sonic.
The flow over a cylinder is a two dimensional flow. When there is a flow over a cylinder, the flow moves upwards and downwards.
The flow over a cylinder is a three dimensional flow. Therefore when there is a flow over a cylinder, it moves upward, downward and also in sideways, left and right.
Therefore, flow over a cylinder has a greater speed than the flow over a sphere. So, to achieve a sonic velocity on the sphere, freestream Mach number is higher than cylinder.
Therefore, critical Mach number of a sphere is higher than cylinder.