TY - JOUR

T1 - To the Problem of Modeling Gas Flows Behind the Strong Shock Wave Front Using an Effective Adiabatic Index

AU - Bogatko, V.I.

AU - Potekhina, E.A.

N1 - Bogatko, V.I., Potekhina, E.A. To the Problem of Modeling Gas Flows Behind the Strong Shock Wave Front Using an Effective Adiabatic Index. Vestnik St.Petersb. Univ.Math. 53, 77–81 (2020). https://doi.org/10.1134/S1063454120010033

PY - 2020/3/26

Y1 - 2020/3/26

N2 - Abstract: In problems involving strong shock waves (the problem of a strong explosion, the motion of bodies with large supersonic speeds, and the problem of supersonic piston expansion), a significant increase in temperature occurs in the disturbed flow region. It is therefore necessary to take the real properties of the gas into account when determining the parameters of the gas flow behind the front of a strong shock wave. This significantly complicates the construction of approximate analytical solutions. However, studies show that the effect of the real properties of the gas on the gas-dynamic parameters of the flow can be taken into account by changing the adiabatic index, i.e., by introducing an effective adiabatic index. If the gas behind the shock wave is in a state of thermodynamic equilibrium, then the effective adiabatic index changes insignificantly in the entire flow zone. This allows us to simulate the flow behind the shock wave front using some perfect gas, whose adiabatic index is determined by the shock wave front depending on the Mach number and the thermodynamic state of the gas. To obtain more accurate solutions for problems with strong shock waves, the model must allow a discontinuity in the adiabatic index at the shock wave. An explicit expression for gas parameters behind the front of an intense shock wave is obtained in this study under the assumption that the adiabatic index undergoes discontinuity during the transition of gas particles through the shock wave surface. Plane and axisymmetric cases are considered.

AB - Abstract: In problems involving strong shock waves (the problem of a strong explosion, the motion of bodies with large supersonic speeds, and the problem of supersonic piston expansion), a significant increase in temperature occurs in the disturbed flow region. It is therefore necessary to take the real properties of the gas into account when determining the parameters of the gas flow behind the front of a strong shock wave. This significantly complicates the construction of approximate analytical solutions. However, studies show that the effect of the real properties of the gas on the gas-dynamic parameters of the flow can be taken into account by changing the adiabatic index, i.e., by introducing an effective adiabatic index. If the gas behind the shock wave is in a state of thermodynamic equilibrium, then the effective adiabatic index changes insignificantly in the entire flow zone. This allows us to simulate the flow behind the shock wave front using some perfect gas, whose adiabatic index is determined by the shock wave front depending on the Mach number and the thermodynamic state of the gas. To obtain more accurate solutions for problems with strong shock waves, the model must allow a discontinuity in the adiabatic index at the shock wave. An explicit expression for gas parameters behind the front of an intense shock wave is obtained in this study under the assumption that the adiabatic index undergoes discontinuity during the transition of gas particles through the shock wave surface. Plane and axisymmetric cases are considered.

KW - modeling

KW - shock wave

KW - hypersonic flows

KW - discontinuity of the adiabatic index

KW - modeling

KW - shock wave

KW - hypersonic flows

KW - discontinuity of the adiabatic index

UR - http://www.scopus.com/inward/record.url?scp=85082601199&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/ce4ed5b8-a9c2-3d4e-8dc9-11c244cc966f/

U2 - 10.1134/S1063454120010033

DO - 10.1134/S1063454120010033

M3 - Article

AN - SCOPUS:85082601199

VL - 53

SP - 77

EP - 81

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 1

ER -