Analytic formulation and numerical implementation of an acoustic pressure gradient prediction

Seongkyu Lee, Kenneth S. Brentner, F. Farassat, Philip J. Morris

Research output: Contribution to journalArticlepeer-review

94 Scopus citations


Two new analytical formulations of the acoustic pressure gradient have been developed and implemented in the PSU-WOPWOP rotor noise prediction code. The pressure gradient can be used to solve the boundary condition for scattering problems and it is a key aspect to solve acoustic scattering problems. The first formulation is derived from the gradient of the Ffowcs Williams-Hawkings (FW-H) equation. This formulation has a form involving the observer time differentiation outside the integrals. In the second formulation, the time differentiation is taken inside the integrals analytically. This formulation avoids the numerical time differentiation with respect to the observer time, which is computationally more efficient. The acoustic pressure gradient predicted by these new formulations is validated through comparison with available exact solutions for a stationary and moving monopole sources. The agreement between the predictions and exact solutions is excellent. The formulations are applied to the rotor noise problems for two model rotors. A purely numerical approach is compared with the analytical formulations. The agreement between the analytical formulations and the numerical method is excellent for both stationary and moving observer cases.

Original languageEnglish (US)
Pages (from-to)1200-1221
Number of pages22
JournalJournal of Sound and Vibration
Issue number3-5
StatePublished - Jan 23 2009

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Acoustics and Ultrasonics
  • Mechanical Engineering


Dive into the research topics of 'Analytic formulation and numerical implementation of an acoustic pressure gradient prediction'. Together they form a unique fingerprint.

Cite this