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

A time evolution analysis is presented for the interaction between the instability waves, shock cells, and screech tones based on the authors' previous numerical simulation database. An attachment and reinforcement 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 in the dominant pressure fluctuations for several typical Mach number screeching jets, it is found that the total number 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 screech tone frequency prediction formula is thus proposed based on this relation. The predicted screech wavelengths or Strouhal numbers of cold and hot jets all agree well with the experimental data by other researchers, except for a small discrepancy for the B mode. It is also noticed that the measured two A0 modes by Ponton et al. [NASA Technical Memorandum No. 113137, Langley Research Center (1997)] can be classified to A1 and A2 modes, respectively, according to the proposed formula.