The dynamics of magnetic flux quanta (Abrikosov vortices) determine the resistive response of superconductors. In pinning-free planar thin films, the penetration and motion of vortices are controlled by edge defects, leading to such arrangements as vortex chains, vortex jets, and phase-slip regimes. Here, relying upon the time-dependent Ginzburg-Landau equation, we predict that these vortex patterns should appear in superconductor open nanotubes even without edge defects, due to the inhomogeneity of the normal magnetic induction component Bn, caused by the three-dimensional (3D) tube geometry. The crossing of the half tubes by dc-driven vortices induces GHz-frequency voltage U oscillations with spectra Uf(B) evolving between nf1 and nmf1 [f1: vortex nucleation frequency; n,m≥2] and blurred in certain ranges of currents and fields. An nf1 spectrum corresponds to a single vortex-chain regime typical for low B and for tubes of small radii. At higher fields, an nmf1 spectrum points to the presence of m vortex chains in the vortex jets which, in contrast to planar thin films, are not diverging because of constraint to the tube areas where Bn is close to maximum. A blurry spectrum implies complex arrangements of vortices because of multifurcations of their trajectories. Finally, due to a stronger confinement of single vortex chains in tubes of small radii, we reveal peaks in dU/dB and jumps in the frequency of microwave generation, which occur when the number of fluxons moving in the half tubes increases by one. In all, our findings are essential for novel 3D superconductor devices which can operate in few- and multifluxon regimes.