We carried out a series of numerical simulations of the unsteady three-dimensional swirling flow in an open tube with a paraxial time-dependent heat source under conditions that induce generation of the central recirculation zone and the precessing vortex core (PVC). Because such flows are known to be high-turbulent, adequacy of turbulent models based on Boussinesq hypothesis (Spalart-Allmaras, k-ε, Standard and SST k-ω) and Reynolds Stress Transport approach (RSM) were tested. It was shown that accounting of the effects of streamline curvature and system rotation is crucial in such modeling. Using results of simulation we study precession frequency of PVC in dependence on the type of source (step-function or sine signal), on the heat source power, frequency and position along the tube axis. It was shown that by the modulation frequency of source power close to frequency of sound standing wave dramatic change of oscillation of flow parameters occurs.