Finite volume simulation of 2-D and 3-D non-stationary magnetogasdynamic flow

This work presents the development of the ideal and real magnetogasdynamic (MGD) equations in two and three spatial dimensions, followed by a modern numerical resolution method. The equations that govern the MGD flows are continuity, momentum, energy and magnetic induction together with a state equation. The method of Roe has been applied, in a high resolution Total Variation Diminishing scheme, with modifications proposed by Yee et al. For the implementation of this method in finite volumes a FORTRAN code has been developed, and it has been applied to the resolution of the magnetogasdynamic Riemann problem and the Hartman flow. Due to the high computational cost demanded by a 3D simulation, it has been necessary to reduce the grid density, compared to that used on the unidimensional and bidimensional cases. In order to evaluate this last issue, an analysis of the effect of the grid density on the results has been included at the end of the present work. The magnetogasdynamic shock tube and the Hartman flow, used as “benchmarks”, have been satisfactorily solved.Grupo Fluidodinámica Computaciona

Finite volume simulation of 2-D and 3-D non-stationary magnetogasdynamic flow

This work presents the development of the ideal and real magnetogasdynamic (MGD) equations in two and three spatial dimensions, followed by a modern numerical resolution method. The equations that govern the MGD flows are continuity, momentum, energy and magnetic induction together with a state equation. The method of Roe has been applied, in a high resolution Total Variation Diminishing scheme, with modifications proposed by Yee et al. For the implementation of this method in finite volumes a FORTRAN code has been developed, and it has been applied to the resolution of the magnetogasdynamic Riemann problem and the Hartman flow. Due to the high computational cost demanded by a 3D simulation, it has been necessary to reduce the grid density, compared to that used on the unidimensional and bidimensional cases. In order to evaluate this last issue, an analysis of the effect of the grid density on the results has been included at the end of the present work. The magnetogasdynamic shock tube and the Hartman flow, used as “benchmarks”, have been satisfactorily solved.Grupo Fluidodinámica Computaciona

Magnetogasdynamic Flow Control of a Mach Reflection

Two-dimensional regular and Mach reflections have been studied in the Mach 4.96 dual-solution domain for a 25° and 26° double-fin inlet. The steady-state computational Mach and regular reflections were subjected to magnetogasdynamic forces to determine whether these forces could be used as a possible flow control mechanism. The numerical code employed for this research solved the inviscid Euler equations with added source terms for the ponderomotive force and accompanying energy interactions. The 25° regular reflection was determined to be extremely sensitive to a decelerating Lorentz force. Transient application of the force led to the transition of the regular reflection to a Mach reflection, increasing the total pressure losses and decreasing the compression ratio. Sustained application of the force resulted in inlet unstart. An accelerating Lorentz force was also examined with the goal of transitioning the 26° Mach reflection to a more efficient regular reflection. The location of the accelerating force and the parameters governing its magnitude were examined. Such forces push the Mach reflection back to a more stable location and reduce the Mach stem height. For the interaction parameters considered, fully regular reflections were not obtained. However, the accelerating Lorentz force proved capable of increasing the total pressure recovery and the static pressure compression beyond the regular reflection values

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

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

One-dimensional MHD flows with cylindrical symmetry: Lie symmetries and conservation laws

A recent paper considered symmetries and conservation laws of the plane one-dimensional flows for magnetohydrodynamics in the mass Lagrangian coordinates. This paper analyses the one-dimensional magnetohydrodynamics flows with cylindrical symmetry in the mass Lagrangian coordinates. The medium is assumed inviscid and thermally non-conducting. It is modeled by a polytropic gas. Symmetries and conservation laws are found. The cases of finite and infinite electric conductivity need to be analyzed separately. For finite electric conductivity $\sigma (\rho,p)$ we perform Lie group classification, which identifies $\sigma (\rho,p)$ cases with additional symmetries. The conservation laws are found by direct computation. For cases with infinite electric conductivity variational formulations of the equations are considered. Lie group classifications are obtained with the entropy treated as an arbitrary element. A variational formulation allows to use the Noether theorem for computation of conservation laws. The conservation laws obtained for the variational equations are also presented in the original (physical) variables

Electrode current distributions in MGD CHANNELS

Current distribution to and electric field behavior of segmented electrodes in linear magnetogasdynamic generato

Invariant Finite-Difference Schemes for Cylindrical One-Dimensional MHD Flows with Conservation Laws Preservation

On the basis of the recent group classification of the one-dimensional magnetohydrodynamics (MHD) equations in cylindrical geometry, the construction of symmetry-preserving finite-difference schemes with conservation laws is carried out. New schemes are constructed starting from the classical completely conservative Samarsky-Popov schemes. In the case of finite conductivity, schemes are derived that admit all the symmetries and possess all the conservation laws of the original differential model, including previously unknown conservation laws. In the case of a frozen-in magnetic field (when the conductivity is infinite), various schemes are constructed that possess conservation laws, including those preserving entropy along trajectories of motion. The peculiarities of constructing schemes with an extended set of conservation laws for specific forms of entropy and magnetic fluxes are discussed.Comment: 29 pages; some minor fixes and generalizations + Appendix containing an additional numerical schem