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Shock Wave Reflections in Unsteady Flows

  • Gabi Ben-Dor

Abstract

Unlike the shock reflection phenomena in pseudo-steady flows (chapter 2) and in steady flows (chapter 3), where the flow fields basically depend on two independent variables, namely; x/t and y/t in the former and x and y in the latter, here the flow field depends on three parameters x, y and t. For this reason, the analytical consideration of the reflection phenomenon in unsteady flows is much more difficult and as a matter of fact very limited progress has been made.

Keywords

Shock Wave Wedge Angle Incident Shock Wave Mach Stem Mach Reflection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols

Latin Letters

ai

local speed of sound in state (i)

Aij

ai/aj

Lm

length of the Mach stem in MR

Lr

length of the reflected shock wave in TRR

m3

flow mass in region (3) of a TRR

Mi

flow Mach number in state (i)

Mm

Mach stem Mach number

Ms

incident shock wave Mach number

R

radius of curvature of cylindrical wedges

s

coordinate along the cylindrical wedge surface

S

propagation distance of the corner-generated signals

t

time

ui

flow velocity in state (i) with respect to R in RR and TRR andTinMR

Vi

flow velocity in state (i) in a laboratory frame of reference

Vij

Vi/aj

Vn

normal shock wave velocity of a TRR with respect to the reflection point R

xtr

x coordinate of the MR→RR transition point

XT

x coordinate of the triple point of an MR

y

distance from Q to P in a TRR

YT

y coordinate of the triple point of an MR

z

distance from R to Q in a TRR

Greek Letters

α

angle between the incident shock wave and the reflecting wedge surface in a TRR

β

angle between the slipstream and the reflecting wedge surface in a TRR

γ

specific heat capacities ratio

Δt

time interval

Δθw

change of the slope of the reflecting surface of a double wedge

θ

angular position of a flow particle

θT

angular position of the triple point

θw

reflecting wedge angle

θw1

wedge angle of the first surface of a double wedge

θw2

wedge angle of the second surface of a double wedge

θwinitial

wedge angle of a cylindrical concave or convex wedge

θwtr

transition wedge angle

θwMtr

transition wedge angle for shock wave Mach number M

θw[A⇔B]

transition wedge angle from reflection A to reflection B

ρi

flow density in state (i)

Φi

angle of incidence between the flow and the oblique shock wave across which the flow enters state (i) with respect to R in RR and TRR and with respect to T in MR.

χ

triple point trajectory angle

χg

triple point trajectory angle at glancing incidence

χtr

triple point trajectory angle at transition

Subscripts

0

flow state ahead of the incident shock wave, i

1

flow state behind the incident shock wave, i

2

flow state behind the reflected shock wave, r

3

flow state behind the Mach stem, m, of an MR or the normal shock wave, n, of a TRR

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Reference

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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Gabi Ben-Dor
    • 1
  1. 1.Department of Mechanical EngineeringBen-Gurion University of the NegevBeer-ShevaIsrael

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