A Study of One-dimensional Weak Shock Propagation Under the Action of Axial and Azimuthal Magnetic Field: An Analytical Approach

The present paper presents an analytical study of the one-dimensional weak shock wave problem in a perfect gas under the action of a generalized magnetic field subjected to weak shock jump conditions (R-H conditions). The magnetic field is considered axial and azimuthal in cylindrically symmetric configuration. By considering a straightforward analytical approach, an explicit solution exhibiting time-space dependency for gas-dynamical flow parameters and total energy (generated during the propagation of the weak shock from the center of the explosion) has been obtained under the significant influence of generalized magnetic fields (axial and azimuthal) and the results are analyzed graphically. From the outcome, it is worth noticing that for an increasing value of Mach number under the generalized magnetic field, the decay process of physical parameters (density, pressure, and magnetic pressure) is a bit slower, whereas the velocity profile and total energy increase rapidly with respect to time. Moreover, for increasing values of Shock-Cowling number the total energy grows rapidly with respect to time

Approximate Analytical Solution using Power Series Method for the Propagation of Blast Waves in a Rotational Axisymmetric non-ideal Gas

In this paper, the propagation of the blast (shock) waves in non-ideal gas atmosphere in rotational medium is studied using a power series method in cylindrical geometry. The flow variables are assumed to be varying according to the power law in the undisturbed medium with distance from the symmetry axis. To obtain the similarity solution, the initial density is considered as constant in the undisturbed medium. Approximate analytical solutions are obtained using Sakurai's method by extending the power series of the flow variables in power of ${\left( {\frac{{{a_0}}}{U}} \right)^2}$, where $U$ and $a_0$ are the speeds of the shock and sound, respectively, in undisturbed fluid. The strong shock wave is considered for the ratio ${\left( {\frac{{{a_0}}}{U}} \right)^2}$ which is considered to be a small quantity. With the aid of that method, the closed-form solutions for the zeroth-order approximation is given as well as first-order approximate solutions are discussed. Also, with the help of graphs behind the blast wave for the zeroth-order approximation, the distributions of variables such as density, radial velocity, pressure and azimuthal fluid velocity are analyzed. The results for the rotationally axisymmetric non-ideal gas environment are compared to those for the ideal gas atmosphere

The Teaching of Gas Dynamics in the National University of Cordoba - UNC

This paper presents the teaching and research activities carried out at the National University of Cordoba (UNC) on issues directly related to Gas Dynamics. Currently, this University offers three courses on this subject: Gas Dynamics I, Gas Dynamics II and Advanced Gas Dynamics. The first two correspond to undergraduate studies, while the third to graduate studies. Gas Dynamics I is a required subject for all Aeronautical Engineering students at UNC, and represents the most advanced degree course within the area of Fluid Mechanics taught at the Department of Aeronautics. While Gas Dynamics II is an elective course that is only taken by students who are interested in deepening concepts in compressible flows. On the other hand, Advanced Gas Dynamics is a valid course for the Aerospace Master´s Degree and the Doctorate in Engineering Sciences. In addition, the growth in activity at the UNC in recent years stands out, both in the number of professors trained in the area, as well as in the number of Undergraduate, Master and Doctoral Theses and in the number of research projects.Fil: Elaskar, Sergio Amado. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Estudios Avanzados en Ingeniería y Tecnología. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto de Estudios Avanzados en Ingeniería y Tecnología; ArgentinaFil: Cid, Guillermo. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas, Físicas y Naturales. Departamento de Aeronáutica; ArgentinaFil: Schulz, Walkiria. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Estudios Avanzados en Ingeniería y Tecnología. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto de Estudios Avanzados en Ingeniería y Tecnología; Argentina. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas, Físicas y Naturales. Departamento de Aeronáutica; Argentin

Converging Cylindrical Shock Waves in a Nonideal Gas With an Axial Magnetic Field

This paper analyses the propagation of converging cylindrical shock waves in a nonidealgas, in the presence of an axial magnetic field. Chester-Chisnell-Whitham’s method has beenemployed to determine the shock velocity and the other flow-variables just behind the shockin the cases, when (i) the gas is weakly ionised before and behind the shock front, (ii) the gasis strongly ionised before and behind the shock front, and (iii) nonionised gas undergoes intenseionisation as a result of the passage of the shock. The effects of the nonidealness of the gas,the conductivity of the gas, and the axial magnetic field have been investigated. It is found thatin the case (i), an increase in the value of parameter ( ) characterising the nonidealness of thegas accelerates the convergence of the shock. In the case (ii), the shock speed and pressurebehind the shock increase very fast as the axis is approached; and this increase occurs earlierif the strength of the initial magnetic field is increased. In the case (iii), for smaller values of theinitial magnetic field, the shock speed, and pressure behind the shock decrease very fast afterattaining a maximum; and for higher values of the initial magnetic field, the tendency of decreaseappears from the beginning. This shows that the magnetic field has damping effect on the shockpropagation. In the case (iii), it was also found that the growth of the shock in the initial phaseand decay in the last phase were faster when it was converging in a nonideal gas in comparisonwith that in a perfect gas. Further, it has been shown that the gas-ionising nature of the shockhas damping effect on its convergence

Research and Reviews: Journal of Pure and Applied Physics Converging Cylindrical Detonation Waves In An Ideal Gas With An Azimuthal Magnetic Field

ABSTRACT This paper analyses the propagation of converging cylindrical detonation waves in an ideal gas with varying initial density and varying azimuthal magnetic field. The Chester-Chisnell-Whitham (CCW) method was employed to determine the detonation front velocity and the other flow-variables just be-hind the shock in the case when (i) the gas is weakly ionized before and behind the detonation front, (ii) the gas is strongly ionized before and behind the detonation front and (iii) nonionized (or weakly ionized)gas undergoes intense ionization as a result of the passage of the detonation front. It is investigated that in case (i) an increase in the value of the strength of initial magnetic field (M −2 cj ) shows almost negligible effect on the convergence of the detonation front and the pressure behind it, while an increase in the value of ratio of specific heats of the gas (γ), increases the velocity of detonation front and the pressure behind it near the axis. A decrease in the value of index for variable density α, accelerates the convergence of front and increases pressure behind it. In the case (ii) on increasing (M −2 cj ), when α = 0, the front velocity near the axis and the pressure behind it decrease. A decrease in the value of α increases the velocity of the detonation front and the pressure behind it. An increase in the value of γ in non-magnetic case, rapidly increases the velocity of detonation front and the pressure behind it. In the case (iii), the variation of M −2 cj and α, show similar behaviour as in case (ii), but an increase in the value of γ rapidly increases the pressure behind the detonation front

Self-Similar Motion of Strong Converging Cylindrical and Spherical Shock Waves in Non-Ideal Stellar Medium

A theoretical model for strong converging cylindrical and spherical shock waves in non-ideal gas characterized by the equation of state (EOS) of the Mie-Gruneisen type is investigated. The governing equations of unsteady one dimensional compressible flow including monochromatic radiation in Eulerian hydrodynamics are considered. These equations are reduced to a system of ordinary differential equations (ODEs) using similarity transformations. Shock is assumed to be strong and propagating into a medium according to a power law. In the present work, two different equations of state (EOS) of Mie-Gruneisen type have been considered and the cylindrical and spherical cases are worked out in detail. The complete set of governing equations is formulated as finite difference problem and solved numerically using MATLAB. The numerical technique applied in this paper provides a global solution to the problem for the flow variables, the similarity exponent α for different Gruneisen parameters. It is observed that increase in measure of shock strength β(ρ/ρ_0 ) has effect on the shock front. The velocity and pressure behind the shock front increases quickly in the presence of the monochromatic radiation and decreases gradually. A comparison between the results obtained for non-ideal and perfect gas in the presence of monochromatic radiation has been illustrated graphically

OpenFOAMTM simulation of the shock wave reflection in unsteady flow

This work studies the impact of a shock wave traveling with non-constant velocity over straight surfaces, generating an unsteady and complex reflection process. Two types of shock waves generated by sudden energy released are studied: cylindrical and spherical. Several numerical tests were developed considering different distances between the shock wave origin and the reflecting surface. The Kurganov, Noelle, and Petrova (KNP) scheme implemented in the rhoCentralFoam solver of the OpenFOAMTM software is used to reproduce the different shock wave reflections and their transitions. The numerical simulations of the reflected angle, Mach number of the shock wave, and position of the triple point are compared with pseudo-steady theory numerical and experimental studies. The numerical results show good accuracy for the reflected angle and minor differences for the Mach number. However, the triple point position is more difficult to predict. The KNP scheme in the form used in this work demonstrates the ability to capture the phenomena involved in the unsteady reflections.Fil: Monaldi, Lucas. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Estudios Avanzados en Ingeniería y Tecnología. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto de Estudios Avanzados en Ingeniería y Tecnología; Argentina. Universidad Nacional de Córdoba; ArgentinaFil: Gutierrez Marcantoni, Luis Felipe. Fundación Universitaria Los Libertadores; Colombia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Estudios Avanzados en Ingeniería y Tecnología. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto de Estudios Avanzados en Ingeniería y Tecnología; ArgentinaFil: Elaskar, Sergio Amado. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Estudios Avanzados en Ingeniería y Tecnología. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto de Estudios Avanzados en Ingeniería y Tecnología; Argentina. Universidad Nacional de Córdoba; Argentin