Computational flow analysis of a cyclone vacuum cleaner can provide valuable fluid mechanics information for efficient design and operation. The vacuum cleaner is made of multiple cones, each with a rotational flow field that facilitates the dust collection. Reliable computational analysis requires both accurate representation of the complex geometry and high-resolution representation of the boundary layers near the internal surfaces of the cones. We address these computational challenges with the Space–Time Variational Multiscale (ST-VMS) method and isogeometric discretization, using NURBS basis functions. The ST framework has higher-order accuracy in general, and the VMS feature of the ST-VMS addresses the challenge created by the turbulent nature of the flow. The isogeometric discretization provides a more accurate representation of the geometry and increased accuracy in the flow solution. We conduct our studies for both single-cone and multi-cone configurations, and the comparison of the results from the two helps us discern the reasonableness of using single-cone flow analysis in place of full-machine flow analysis.