42nd AIAA Aerospace Sciences Meeting and Exhibit 5-8 January 2004, Reno, Nevada AIAA 2004-256 AIAA 2004-0256 Receptivity to Freestream Disturbances of a Mach 0 Nonequilibrium Reacting Oxygen Flow over A Flat Plate Yanbao Ma and Xiaolin Zhong University of California, Los Angeles January 5 8, 2004 / Reno, NV For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics 80 Alexander Bell Drive, Suite 500, Reston, Virginia 209-4344 Copyright 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
8.0 T / T 5.0 T (perfect gas) T (nonequilibrium flow) T v (nonequilibrium flow) 0.0 M 9.5 M 2 (perfect gas) M 2 (nonequilibrium flow) Shock position (perfect gas) Shock position (nonequilibrium flow) 0.2 0.0 2.0 9.0 0.08 6.0 9.0 0.06 3.0 8.5 0.04 0.02 0.0 0 40 80 20 60 y / L 8.0 0.00.0 2.4 u / u 0.9 0.8 p / p 2.2 2.0 0.7 0.6 0.5 Perfect gas Nonequilibrium flow.8.6 Perfect gas Nonequilibrium flow 0.4 0.3 0.2.4 0..2 0.0 0 40 80 20 60 y / L.0 T / T 8.0 6.0 p / p.8.6 Perfect gas Nonequilibrium flow 4.0 Perfect gas Nonequilibrium flow (T) Nonequilibrium flow (T v ).4 2.0.2 0.0.0 0 30 60 90 20 50 80 y / L
C o 0.08 0.06.2 a / u. mode I () (F = 5.0e-5) mode I (2) (F = 5.0e-5) Mack modes (F = 5.0e-5) mode I () (F = 3.98e-5) mode I (2) (F = 3.98e-5) Mack modes (F = 3.98e-5) + M 0.04 st mode 2nd mode 0.02 0.9 - M 0.00 0.8 0 0.05 0. ω 0.06 C o 0.00 α i 0.008 mode I () (F = 5.0e-5) mode I (2) (F = 5.0e-5) Mack modes (F = 5.0e-5) mode I () (F = 3.98e-5) mode I (2) (F = 3.98e-5) Mack modes (F = 3.98e-5) + M 0.04 0.006 0.004 0.02 0.002 - M 0.00 0 40 80 20 60 y / L 0.000 st mode 2nd mode -0.002 0 0.05 0. ω F 5.0E-4 4.0E-4 3.0E-4 F = 0.825e-4 F = 0.5e-4 4.0E-04 3.0E-04 n= n= 2 n= 3 n= 4 n= 5 2.0E-4 2.0E-04.0E-4.0E-04 0.0E0 0 500 000 500 2000 R
3.2E-03 6.0E-04 2.4E-03 n= 6 n= 7 n= 8 n= 9 n=0 4.5E-04 n= 6 n= 7 n= 8 n= 9 n=0.6e-03 3.0E-04 8.0E-04.5E-04.6E-03.2E-03 n= n=2 n=3 n=4 n=5 2.8E-04 n= n=2 n=3 n=4 n=5 2.E-04 8.0E-04.4E-04 4.0E-04 7.0E-05 2.0E-04.5E-04 n= n= 2 n= 3 n= 4 n= 5 a / u.2 LST (mode I ()) LST (Mack modes) Simulation (Mack modes) Simulation (mode I). + M.0E-04 st mode 5.0E-05 0.9 - M 0.8
a / u.2 LST (mode I ()) LST (mode I (2)) LST (Mack modes) Simulation (Mack modes) Simulation (mode I). + M 8.0E-04 6.0E-04 Fast acoustic waves (θ = 0) Perfect gas ( j = ) Nonequilibrium flow ( j = ) Perfect gas ( j = 2 ) Nonequilibrium flow ( j = 2 ) 3.0E-03 2.0E-03 Slow acoustic waves (θ = 0) Perfect gas ( j = ) Nonequilibrium flow ( j = ) Perfect gas ( j = 2 ) Nonequilibrium flow ( j = 2 ) st mode 2nd mode 4.0E-04 0.9 - M 2.0E-04.0E-03 0.8 (a) (b).2 LST (mode I ()) LST (mode I (2)) LST (Mack modes) LST (mode II) Simulation (Mack modes) Simulation (mode I). a / u + M.2 a / u. Fast acoustic waves (θ = 0) LST (mode I ()) LST (mode I (2)) LST (Mack modes) DNS (perfect gas) DNS (nonequilibrium flow) + /M.2 a / u. Slow acoustic waves (θ = 0) LST (mode I ()) LST (mode I (2)) LST (Mack modes) DNS (perfect gas) DNS (nonequilibrium flow) + /M st mode 2nd mode st mode 2nd mode 2nd mode 0.9 - M 0.9 - /M 0.9 -/ M 0.8 (a) 0.8 (b) 0.8 2.0E-03 α i.0e-03 LST (n = 8) LST (n = 8) LST (n = 8) DNS (n = 8) DNS (n = 0) DNS (n = 5) 36.0 u u r (Simulation) 8.0 u i (Simulation) u r (2nd mode, LST) u i (2nd mode, LST) 0.0-8.0-36.0 0 30 60 90 y / L20 (a) 30.0 v v r (Simulation) 20.0 v i (Simulation) v r (2nd mode, LST) 0.0 v i (2nd mode, LST) 0.0-0.0 0 30 60 90 y / L20 (b).5 p.0 0.5 0.0-0.5 p r (Simulation) p i (Simulation) p r (2nd mode,lst) p i (2nd mode,lst) 8E3 T 4E3 0E0 T r (Simulation) T i (Simulation) T r (2nd mode,lst) T i (2nd mode, LST) -.0E-03 -.0 0 30 60 90 y / L20 (c) -4E3 0 30 60 90 y / L20 (d) -2.0E-03
7.5E-04 5.0E-04 Fast acoustic waves (perfect gas) θ = 0 o θ = 22.5 o θ = 45 o θ = 67.5 o 7.5E-04 5.0E-04 Fast acoustic waves (nonequilibrium flow) θ = 0 o θ = 22.5 o θ = 45 o θ = 67.5 o.6e-03.2e-03 8.0E-04 Fast acoustic waves (pefect gas) n= n= 2 n= 3 n= 4 n= 5.6E-03.2E-03 8.0E-04 Fast acoustic waves (nonequilibrium flow) 2.5E-04 0 0. 0.2 0.3 0.4 0.5 (a) 0.6 0.7 0.8 0.9 2.5E-04 0 0. 0.2 0.3 0.4 0.5 0.6 0.7 0.8 (b) 4.0E-04 (a) 4.0E-04 n= n= 2 n= 3 n= 4 n= 5 (b).5e-03.0e-03 Slow acoustic waves (perfect gas) θ = 0 o θ = 22.5 o θ = 45 o θ = 67.5 o 2.4E-03.8E-03 Slow acoustic waves (nonequilibrium flow) θ = 0 o θ = 22.5 o θ = 45 o θ = 67.5 o.6e-03.2e-03 Fast acoustic waves (pefect gas) n= 6 n= 7 n= 8 n= 9 n=0.6e-03.2e-03 Fast acoustic waves (nonequilibrium flow) n= 6 n= 7 n= 8 n= 9 n=0.2e-03 8.0E-04 8.0E-04 5.0E-04 6.0E-04 4.0E-04 4.0E-04 (a) 0 0. 0.2 0.3 0.4 0.5 0.6 0.7 0.8 (b) (c) (d) 5 Response coefficient (K s ) 0 5 Receptivity to slow acoustic waves Perfect gas Noequibrium flow 6.0E-04 4.5E-04 3.0E-04 Fast acoustic waves (pefect gas) n= n=2 n=3 n=4 n=5 6.0E-04 4.5E-04 3.0E-04 Fast acoustic waves (nonequilibrium flow) n= n=2 n=3 n=4 n=5.5e-04.5e-04 0 0 22.5 45 67.5 90 θ (degree) (e) (f)
.5E-03 Slow acoustic waves (pefect gas).5e-03 Slow acoustic waves (nonequilibrium flow).0e-03.0e-03 n= n= 2 n= 3 n= 4 n= 5 5.0E-04 n= n= 2 n= 3 n= 4 n= 5 (a) 5.0E-04 (b) 25 Receptivity to slow acoustic waves Pefect gas Noequilibrium flow 5.0E-03 4.0E-03 3.0E-03 2.0E-03 Slow acoustic waves (pefect gas) n= 6 n= 7 n= 8 n= 9 n=0 5.0E-03 4.0E-03 3.0E-03 2.0E-03 Slow acoustic waves (nonequilibrium flow) n= 6 n= 7 n= 8 n= 9 n=0 Response coefficient (K s ) 20 5 0.0E-03.0E-03 5 (c) (d) 0 00 50 200 250 f* (k Hz) 2.0E-03.5E-03 Slow acoustic waves (pefect gas) n= n=2 n=3 n=4 n=5 2.0E-03.5E-03 Slow acoustic waves (nonequilibrium flow) n= n=2 n=3 n=4 n=5.0e-03.0e-03 5.0E-04 5.0E-04 (e) (f)