1 47th Aerospace Sciences Meeting - Orlando W. Engblom, D. Goldstein AIAA Acoustic Analogy for Oscillations Induced by Supersonic Flow over a Forward-Facing Nose Cavity

2 47th Aerospace Sciences Meeting - Orlando Background (Animation)  “Deep” cavities produce strong self-sustained oscillations  “Shallow” cavities amplify freestream disturbances

3 47th Aerospace Sciences Meeting - Orlando Background (Applications) Anti-tank penetrator (kinetic energy weapon)  Numerical and experimental evidence that adding forward-facing nose cavity delays ablation (Silton & Goldstein, JFM, 2000)  Detect freestream disturbances (instability waves?); Other applications?  Mechanisms behind resonance/amplification not well enough understood

4 47th Aerospace Sciences Meeting - Orlando Objectives  Develop an acoustic analogy to describe forward-facing cavity behaviour –Limit to noise-driven cavity geometries (“small disturbances”) –Limit to perturbations at discrete frequency  Parametrically evaluate cavity behaviour using both SMD (spring-mass- damper) and CFD (Navier-Stokes) models: –Amplification (G) is measure of oscillation strength (pressure fluctuations): L/DA (%)MM D n /D 0.25     DnDn

5 47th Aerospace Sciences Meeting - Orlando Methodology (CFD)  CFD solver (TESTBED)  Finite-volume, density-based, multi-block structured  2 nd -order spatial Van Leer, pressure-switch limiter  2 nd -order time advancement: Implicit point-based Gauss- Seidel with subiterations  MPI parallel-processing capability  Numerical procedure  Typically 50 cavity oscillations simulated in 4 hours before pseudo-steady  Typically required 10 subiterations to converge at each time step to tolerance of 1e-5

6 47th Aerospace Sciences Meeting - Orlando Methodology (CFD) L/D=0.75 D n /D=2 L/D=0.25 D n /D=2 L/D=1.10 D n /D=2 L/D=0.75, D n /D=4 L/D=0.75, D n /D=8 centerline Hemispherical nose plus cylindrical cavity (every other grid point removed) BASELINE

7 47th Aerospace Sciences Meeting - Orlando CFD Validation  Validate TESTBED (Navier-Stokes solver) against recent and relevant experimental data from Purdue Forward-facing cavity model tested in PQFLT PQFLT CFD M  = 4 p  = 363 Pa T  = 70.7K

8 47th Aerospace Sciences Meeting - Orlando CFD Validation Normalized rms pressure ratios (CFD) Basewall pressure histories (CFD) Note: Peak p rms similar to that found at M  =5 (Engblom and Goldstein)

9 47th Aerospace Sciences Meeting - Orlando Animation: M  =5, L/D=0.75, ±3% L/DA (%)MM D n /D 0.25    

10 47th Aerospace Sciences Meeting - Orlando Acoustic Analog Development Chamber Neck Sound radiated Flow direction Chamber Neck Flow direction (finite medium) (infinite medium) Helmholtz Resonator: Supersonic Flow over Nose Cavity: Treat cavity as mass which accelerates according to mean dp/dx = (p base -p input )/L

11 47th Aerospace Sciences Meeting - Orlando Acoustic Analog Development Natural frequency: Cavity mass/area: Cavity stiffness: Driving force/area: Spring force/area:

12 47th Aerospace Sciences Meeting - Orlando Acoustic Analog Development baffle vibrating piston Baffled piston Image piston Bow shock reflector  Baffled-piston radiation: Ref: Morse & Ingard Image-piston effect:

13 47th Aerospace Sciences Meeting - Orlando Acoustic Analog Development Two ODEs to integrate with 4 th -order Runge-Kutta

14 47th Aerospace Sciences Meeting - Orlando SMD vs. CFD Results L/DA (%)MM D n /D 0.25     L/DA (%)MM D n /D 0.25    

15 47th Aerospace Sciences Meeting - Orlando SMD vs. CFD Results L/DA (%)MM D n /D 0.25    

16 47th Aerospace Sciences Meeting - Orlando SMD vs. CFD Results L/DA (%)MM D n /D 0.25    

17 47th Aerospace Sciences Meeting - Orlando SMD vs. CFD Results L/DA (%)MM D n /D 0.25     SMD-2 corrections

18 47th Aerospace Sciences Meeting - Orlando SMD vs. CFD Results L/DA (%)MM D n /D 0.25    

19 47th Aerospace Sciences Meeting - Orlando SMD vs. CFD Results

20 47th Aerospace Sciences Meeting - Orlando Animation: M  =5, L/D=0.75, ±1% noise, D n /D=4 NOTE: G ~ 50 L/D=1.1 D n /D=4

21 47th Aerospace Sciences Meeting - Orlando Discussion: Self-sustained Oscillations  Bow shock oscillations alter the radial relieving effect  Relieving effect reduced during fill phase leading to large “compression” of cavity gas  Relieving effect increased during purge phase leading to large “expansion” of cavity gas  Combined effects above lead to effective “negative dissipation” effect  Recall: primary dissipation effect (radiation resistance) decreases rapidly as cavity depth increases  Thus, self-sustained oscillations develop for sufficiently deep cavities

22 47th Aerospace Sciences Meeting - Orlando Conclusions  Acoustic analog (SMD-2) results compare adequately well to CFD for variations in cavity depth, noise amplitude & frequency, at high M , and for large D n /D  Poor comparison at low M  and for small D n /D suggest first-order physics are missing from analog  Classic baffled-piston type radiation resistance is a primary dissipation mechanism, but is strongly affected by radial convection currents and bow shock reflection effects  Mechanism for self-sustained oscillations is proposed  Amplification of ~50 predicted by CFD (L/D=1.1, D n /D =4)