TY - JOUR
T1 - Shock interactions with heavy gaseous elliptic cylinders
T2 - Two leeward-side shock competition modes and a heuristic model for interfacial circulation deposition at early times
AU - Ray, Jaideep
AU - Samtaney, Ravindra
AU - Zabusky, Norman J.
PY - 2000/1/1
Y1 - 2000/1/1
N2 - We identify two different modes, types I and II, of the interaction for planar shocks accelerating heavy prolate gaseous ellipses. These modes arise from different interactions of the incident shock (IS) and transmitted shock (TS) on the leeward side of the ellipse. A time ratio tτ/tI(M,η,λ,γ 0,γb), which characterizes the mode of interaction, is derived heuristically. Here, the principal parameters governing the interaction are the Mach number of the shock (M), the ratio of the density of the ellipse to the ambient gas density, (η>1), γ0, γb (the ratios of specific heats of the two gases), λ (the aspect ratio). Salient events in shock-ellipse interactions are identified and correlated with their signatures in circulation budgets and on-axis space-time pressure diagrams. The two modes yield different mechanisms of the baroclinic vorticity generation. We present a heuristic model for the net baroclinic circulation generated on the interface at the end of the early-time phase by both the IS and TS and validate the model via numerical simulations of the Euler equations. In the range 1.2≤M≤3.5, 1.54≤η≤5.04, and λ=1.5 and 3.0, our model predicts the baroclinic circulation on the interface within a band of ± 10% in comparison to converged numerical simulations.
AB - We identify two different modes, types I and II, of the interaction for planar shocks accelerating heavy prolate gaseous ellipses. These modes arise from different interactions of the incident shock (IS) and transmitted shock (TS) on the leeward side of the ellipse. A time ratio tτ/tI(M,η,λ,γ 0,γb), which characterizes the mode of interaction, is derived heuristically. Here, the principal parameters governing the interaction are the Mach number of the shock (M), the ratio of the density of the ellipse to the ambient gas density, (η>1), γ0, γb (the ratios of specific heats of the two gases), λ (the aspect ratio). Salient events in shock-ellipse interactions are identified and correlated with their signatures in circulation budgets and on-axis space-time pressure diagrams. The two modes yield different mechanisms of the baroclinic vorticity generation. We present a heuristic model for the net baroclinic circulation generated on the interface at the end of the early-time phase by both the IS and TS and validate the model via numerical simulations of the Euler equations. In the range 1.2≤M≤3.5, 1.54≤η≤5.04, and λ=1.5 and 3.0, our model predicts the baroclinic circulation on the interface within a band of ± 10% in comparison to converged numerical simulations.
UR - http://www.scopus.com/inward/record.url?scp=0034036740&partnerID=8YFLogxK
U2 - 10.1063/1.870276
DO - 10.1063/1.870276
M3 - Article
AN - SCOPUS:0034036740
VL - 12
SP - 707
EP - 716
JO - Physics of Fluids
JF - Physics of Fluids
SN - 1070-6631
IS - 3
ER -