Geodesic
Flow structure behind a~shock wave in a~channel with periodically arranged obstacles
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems and methods in mechanics, Tome 300 (2018), pp. 216-228

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We study the propagation of a pressure wave in a rectangular channel with periodically arranged obstacles and show that a flow corresponding to a discontinuity structure may exist in such a channel. The discontinuity structure is a complex consisting of a leading shock wave and a zone in which pressure relaxation occurs. The pressure at the end of the relaxation zone can be much higher than the pressure immediately behind the gas-dynamic shock. We derive an approximate formula that relates the gas parameters behind the discontinuity structure to the average velocity of the structure. The calculations of the pressure, velocity, and density of the gas behind the structure that are based on the average velocity of the structure agree well with the results of gas-dynamic calculations. The approximate dependences obtained allow us to estimate the minimum pressure at which there exists a flow with a discontinuity structure. This estimate is confirmed by gas-dynamic calculations.
Keywords: attenuation of a shock wave, channel with obstacles, traveling wave, interaction of a shock/blast wave with barriers. 
@article{TM_2018_300_a17,
     author = {V. A. Shargatov and A. P. Chugainova and S. V. Gorkunov and S. I. Sumskoi},
     title = {Flow structure behind a~shock wave in a~channel with periodically arranged obstacles},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {216--228},
     publisher = {mathdoc},
     volume = {300},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2018_300_a17/}
}
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V. A. Shargatov; A. P. Chugainova; S. V. Gorkunov; S. I. Sumskoi. Flow structure behind a~shock wave in a~channel with periodically arranged obstacles. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems and methods in mechanics, Tome 300 (2018), pp. 216-228. http://geodesic.mathdoc.fr/item/TM_2018_300_a17/