A multi-mode screech frequency prediction formula for circular supersonic jets

In this paper, a detailed time evolution analysis is presented for the interaction between the instability waves, shock cells and screech tones based on the authors' previous numerical simulation data base. An attachment and merging process of the upstream propagating screech waves with the downstream hydrodynamic waves is identified and recognized as part of the screech loop. The first five shock cells are recognized as the effective sound source region. Through an analysis of the phase variation of the dominant pressure fluctuations for several typical Mach number screeching jets, it is found that the total wave numbers of the instability waves and the upstream feedback sound waves in the effective source region can be identified as 5 for the A1, B and D modes, and 6 for A2 and C modes, respectively. A new screech tone frequency prediction formula is thus proposed based on this relation. The predicted screech wavelengths or Strouhal numbers of the cold and hot jets all agree well with the experimental data by other researchers, except a small discrepancy for the B mode. It is also found that the measured two A0 modes in the experiment by Ponton et al. can be classified to A1 and A2 modes respectively according to the proposed prediction formula.