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Interaction of weak shock waves with perforated metal plates

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Abstract

The interaction of a shock wave with a different number of perforated plates of different permeability and configuration was studied in a shock tube. The Mach numbers of the incident shock wave in the air varied in the range 1.1–1.5, which corresponded to the subsonic gas flow behind it. We used several plates made of aluminium with a thickness of 2 mm, each of which was determined by the permeability 0.13–0.54. The propagation of shock waves was recorded using a Phantom 710 high-speed camera and a shadow device IAB-451. It was shown that the transmitted shock waves passing through the perforated plates with an increase in the Mach number of the incident shock wave attenuate more strongly, and the opposite trend is observed for reflected shock waves. Approximation formulas are proposed that make it possible to estimate the effect of shock wave attenuation by perforated plates with different permeability depending on the Mach number of the incident shock wave. It has been shown that “stratification” of the incident shock wave into many weaker reflected waves during reverberation on the plates and their subsequent addition can eventually lead to the formation of a reflected shock wave in front of a set of perforated plates of the same intensity as reflected from the solid end. It was shown that the maximum effect of attenuation of the transmitted shock wave is recorded when using packets of plates with successively decreasing permeability.

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Abbreviations

#1, #2, #3, #4:

Pressure transducers

DS:

Diagnostic section

f :

Area of a single hole on a plate

F :

Cross area of the diagnostic section

HFB:

Holes for fixing bolts

HPC:

High-pressure chamber

LPC:

Low-pressure chamber

m :

Permeability of single plate

N1...N14:

Model of perforated plate set

PP:

Perforated plate or plates

\(a_1\) :

Initial sound speed

\(a_2\) :

Sound speed behind the incident shock wave

\(M_1\) :

Mach number of incident shock wave

\(M_\mathrm{T}\) :

Mach number of transmitted shock wave

\(M_\mathrm{R}\) :

Mach number of reflected shock wave

\(M^*_\mathrm{R}\) :

Theoretical Mach number of the reflected shock wave

\(P_1\) :

Initial pressure in the low-pressure chamber

\(P_2\) :

Pressure at front of the incident shock wave

\(P^*_2\) :

Theoretical pressure at front of the incident shock wave

\(P_5\) :

Pressure at front of the reflected shock wave

\(P^*_5\) :

Theoretical pressure at front of the reflected shock wave

\(P_\mathrm{TSW}\) :

Pressure of the leading transmitted shock wave

R :

Universal gaseous constant

RBSW:

Reverberation between end wall and back face of the plates

RSW:

Reflected shock wave

R2-SW:

Second reflected shock waves

R3-SW:

Third reflected shock waves

SW:

Incident shock wave

t :

Time

\(T_1\) :

Initial temperature

\(T_2\) :

Temperature behind the incident shock wave

\(t_1\)...\(t_4\) :

Time moments on x-t-diagrams

TSW:

Transmitted shock wave

\(t_\mathrm{SW}\) :

Duration of passage of the incident shock wave between sensors #1 and #2

\(t_\mathrm{TSW}\) :

Duration of passage of the transmitted shock wave between sensors #3 and #4

\(t_\mathrm{RSW}\) :

Duration of passage of the reflected shock wave between sensors #2 and #1

\(u_2\) :

Flow velocity behind the incident shock wave

\(u_\mathrm{T}\) :

Flow velocity behind the transmitted shock wave

\(w_1\) :

Velocity of incident shock wave

\(w_\mathrm{T}\) :

Velocity of transmitted shock wave

\(w_\mathrm{R}\) :

Velocity of reflected shock wave

\(\alpha\) :

Approximation coefficient

\(\beta\) :

Approximation coefficient

\(\gamma\) :

Heat capacity ratio

\(\delta\) :

Pressure attenuation rate for the transmitted shock wave

\(\varepsilon\) :

Approximation coefficient

\(\zeta\) :

Hydraulic resistance

\(\zeta _1\) :

Hydraulic resistance, geometric factor

\(\zeta _2\) :

Hydraulic resistance, gas-dynamic factor

\(\xi\) :

Velocity deficit

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Acknowledgements

This work was supported by the Ministry of Science and Higher Education of the Russian Federation, State Assignment number 075-01056-22-00.

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Author notes

  1. Sergey Golovastov, Anton Mikushkin, Antonina Mikushkina and Yuri Zhilin have contributed equally to this work.

Authors and Affiliations

  1. Physical Gas-Dynamics laboratory, Joint Institute for High Temperatures of RAS, Izhorskaya str., 13, build.2, Moscow, Russia, 125412

    Sergey Golovastov, Anton Mikushkin, Antonina Mikushkina & Yuri Zhilin

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  1. Sergey Golovastov
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  2. Anton Mikushkin
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  3. Antonina Mikushkina
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  4. Yuri Zhilin
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Contributions

S.V. Golovastov processed experiments and prepared the manuscript. A.Yu. Mikushkin performed visualization. A.A. Mikushkina performed pressure measurement. Yu. V. Zhilin provided experiments and developed a theory. All authors contributed equally to analysing data and reaching conclusions and in writing the paper.

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Correspondence to Sergey Golovastov.

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Golovastov, S., Mikushkin, A., Mikushkina, A. et al. Interaction of weak shock waves with perforated metal plates. Exp Fluids 63, 97 (2022). https://doi.org/10.1007/s00348-022-03451-4

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