## 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## List of Symbols

## Latin Letters

- a
_{i} local speed of sound in state (i)

- A
_{ij} a

_{i}/a_{j}- L
_{m} length of the Mach stem in MR

- L
_{r} length of the reflected shock wave in TRR

- m
_{3} flow mass in region (3) of a TRR

- M
_{i} flow Mach number in state (i)

- M
_{m} Mach stem Mach number

- M
_{s} 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

- u
_{i} flow velocity in state (i) with respect to R in RR and TRR andTinMR

- V
_{i} flow velocity in state (i) in a laboratory frame of reference

- V
_{ij} V

_{i}/a_{j}- V
_{n} normal shock wave velocity of a TRR with respect to the reflection point R

- x
^{tr} x coordinate of the MR→RR transition point

- X
_{T} x coordinate of the triple point of an MR

- y
distance from Q to P in a TRR

- Y
_{T} 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

- Δθ
_{w} change of the slope of the reflecting surface of a double wedge

- θ
angular position of a flow particle

- θ
_{T} angular position of the triple point

- θ
_{w} reflecting wedge angle

- θ
_{w}^{1} wedge angle of the first surface of a double wedge

- θ
_{w}^{2} wedge angle of the second surface of a double wedge

- θ
_{w}^{initial} wedge angle of a cylindrical concave or convex wedge

- θ
_{w}^{tr} transition wedge angle

- θ
_{wM}^{tr} transition wedge angle for shock wave Mach number M

- θ
_{w}[A⇔B] transition wedge angle from reflection A to reflection B

- ρ
_{i} flow density in state (i)

- Φ
_{i} 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

- χ
_{g} triple point trajectory angle at glancing incidence

- χ
^{tr} 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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