Shock Wave Reflections in Steady Flows

  • Gabi Ben-Dor
Chapter

Abstract

The analytical investigation of the reflection phenomenon of shock waves in steady flows is much simpler than that in pseudo-steady flows for the following reasons:
  1. 1)

    Unlike the reflection process in pseudo-steady flows, where it is coupled with an additional process, namely, the flow deflection process (see section 2.6.1), in steady flows the reflection process is independent.

     
  2. 2)

    Unlike the analysis of the reflection process in pseudo-steady flows, where there is a need to analytically predict the first triple point trajectory angle, χ, in order to transform the results from the (Ms, \(\theta _w^c\))-plane to the more physically meaningful and more applicable (Ms, θw)-plane, in steady flows the results are presented in the (M01)-plane. The presentation of the results in this plane can be done by solving equations (1.14) to (1.27) without the need for an additional expression for χ [equation (2.33)] as discussed in section 2.2.1.

     
  3. 3)

    Of the ten different shock wave reflection configurations mentioned in section 1.1 only two, namely, RR and SMR, are possible in steady flows.

     

Keywords

Shock Wave Triple Point Incident Shock Incident Shock Wave Reflection Point 
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

k

thermal conductivity

Lm

length of the Mach stem

Lw

length of the reflecting wedge

Mi

flow Mach number in state (i)

Ms

incident shock wave Mach number

pi

static pressure in state (i)

ui

flow velocity in state (i)

Greek Letters

γ

specific heat capacities ratio

δmax(M)

maximum deflection angle for a flow having Mach number M through an oblique shock wave

θw

reflecting wedge angle

γwC

complementary wedge angle

μ

dynamic viscosity

μi

Mach angle of the flow having a Mach number Mi

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)

Φi

limiting angle of incidence

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.

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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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