Aeroacoustic computation of tones generated from low Mach number cavity flows, using a preconditioned method

Open Access
Paul, Brent Steven
Graduate Program:
Doctor of Philosophy
Document Type:
Date of Defense:
October 06, 2016
Committee Members:
  • Philip J. Morris, Dissertation Advisor
  • Philip J. Morris, Committee Chair
  • Victor W. Sparrow, Committee Member
  • Lyle N. Long, Committee Member
  • Laura L. Pauley, Outside Member
  • computational fluid dynamics
  • computational aeroacoustics
  • CFD
  • CAA
  • cavity
  • cavity tone
  • Helmholtz
  • vortex shedding
  • Strouhal
The hydrodynamically generated noise produced from flow over cavities includes both broadband and tones. The frequency content and amplitude of the resulting noise is a function of the cavity geometry and the approaching boundary layer. The cavity length to depth ratio (L/D) is an important parameter that governs the characteristics of cavity noise generated. While both of the noise components are important this work will focus on the production of cavity tones. Cavity tones typically have higher sound pressure levels and can propagate over longer distances than the broadband noise. The enhancements to the numerical code shown in this work result in the first non-hybrid tool for the prediction of low speed cavity noise. At moderate subsonic Mach numbers the direct calculation of cavity tones has been performed by numerous researchers using highly accurate spatial and time discretization. However, most researchers that are trying to predict the noise from low Mach number flows take a hybrid approach where the fluid dynamics of the simulation are solved with a computational fluid dynamics (CFD) solver and the acoustics are solved separately. The other solver is often based on Lighthill’s Acoustic Analogy or an asympototic method such as the Expansion about Incompressible Flow (EIF). This work calculates the conservative Navier-Stokes variables to directly predict the cavity tones. The numerical solver CHOPA (Compressible, High-Order Parallel Acoustics) is extended in this work for the accurate and fast calculation of low Mach number cavity flows. A time-derivative preconditioner equalizes the acoustic wave and turbulence convective speeds to allow for a more efficient time step and shorter calculation times. Because the preconditioner destroys the time accuracy of the solution a dual-time step approach is used for the time integration. Other modifications to the code are required to facilitate the proper implementation of the preconditioner: Matrix-based artificial dissipation, buffer zone, and extrapolation boundary condition. An extension by Buelow of Choi-Merkle’s viscous preconditioner is selected for this work. There are several different numerical validations performed on the preconditioned Navier-Stokes solver to ensure high quality solutions. First, the combination buffer zone/extrapolation boundary condition is tested by simulating the propagation of a Gaussian pressure pulse. Then the preconditioner is tested with several different analyses. The convection of a uniform velocity flow field with a random perturbation imposed on the flow field tests if the preconditioned solution is independent of the flow Mach number. Then a time accurate Gaussian pressure pulse tests the ability of the preconditioner to solve a time dependent solution. Lastly, a laminar boundary layer flow is calculated and compared to an exact solution showing that the preconditioner is effective for viscous flows. The prediction of cavity tones from a deep (L/D = 0.78) and shallow (L/D = 2.35) cavity is simulated for comparison against the experimental measurements of Block. The Mach number of the simulations varied from 0.05 to 0.4. The cavity tone frequencies have an acceptable comparison against the measurements for the deep cavity. However, the shallow cavity tones were almost independent of the flow speed, which may be an indication that standing waves in the cavity could be responsible for the tones for this geometry. The other cavity simulations replicated the experiment by Stallings et al.for L/D = 5.42 and L/D = 6.25 for a Mach number of 0.2. The time-averaged wall pressure fluctuations were compared to measurements. While the predicted wall pressures did not match the experiment the discrepancy is because of the existence of a “wake mode” in the numerical results. This is a two-dimensional phenomenon where a large vortex is generated in the cavity and then violently ejected from the cavity, significantly increasing drag. While not matching the experiment the results behave as expected for a cavity resonating in a wake mode.