A Monolithic Finite Element Formulation for Magnetohydrodynamics Involving a Compressible Fluid

This work develops a new monolithic finite-element-based strategy for magnetohydrodynamics (MHD) involving a compressible fluid based on a continuous velocity–pressure formulation. The entire formulation is within a nodal finite element framework, and is directly in terms of physical variables. The exact linearization of the variational formulation ensures a quadratic rate of convergence in the vicinity of the solution. Both steady-state and transient formulations are presented for two- and three-dimensional flows. Several benchmark problems are presented, and comparisons are carried out against analytical solutions, experimental data, or against other numerical schemes for MHD. We show a good coarse-mesh accuracy and robustness of the proposed strategy, even at high Hartmann numbers.

Characterization of Supersonic Compressible Fluid Flow Using High-Speed Interferometry

This paper presents a very effective interference technique for the sensing and researching of compressible fluid flow in a wind tunnel facility. The developed technique is very sensitive and accurate, yet easy to use under conditions typical for aerodynamic labs, and will be used for the nonintrusive investigation of flutter in blade cascades. The interferometer employs a high-speed camera, fiber optics, and available “of-the-shelf” optics and optomechanics. The construction of the interferometer together with the fiber optics ensures the high compactness and portability of the system. Moreover, single-shot quantitative data processing based on introducing a spatial carrier frequency and Fourier analysis allows for almost real-time quantitative processing. As a validation case, the interferometric system was successfully applied in the research of supersonic compressible fluid discharge from a narrow channel in a wind tunnel. Density distributions were quantitatively analyzed with the spatial resolution of about 50 μm. The results of the measurement revealed important features of the flow pattern. Moreover, the measurement results were compared with Computational Fluid Dynamics (CFD) simulations with a good agreement.

Stationary solutions in thermodynamics of stochastically forced fluids

We study the full Navier–Stokes–Fourier system governing the motion of a general viscous, heat-conducting, and compressible fluid subject to stochastic perturbation. The system is supplemented with non-homogeneous Neumann boundary conditions for the temperature and hence energetically open. We show that, in contrast with the energetically closed system, there exists a stationary solution. Our approach is based on new global-in-time estimates which rely on the non-homogeneous boundary conditions combined with estimates for the pressure.

Studying the interaction of a reservoir with an ideal compressible fluid with an elastic half-space

We solve in a flat formulation the problem of harmonic oscillations for a basin with an ideal compressible fluid on an elastic half-space exposed to a localized surface vibration load. The problem reduces to an integral equation (IE) of the first kind for the amplitude of the contact hydrodynamic pressure with a kernel that depends on the difference and the sum of arguments. The IE was solved by the factorization method. A semi-analytical method is presented for determining the main parameters of the contact interaction in hydroelastic systems «liquid-soil» taking into account the effect of natural and man-made vibration loads on them. This makes it possible to identify the conditions for the occurrence of dynamic modes that are dangerous for the construction integrity and to estimate their frequencies range depending on defining characteristics of the system.

AN INVESTIGATION TURBULENCE MODEL OF STANDARD k- TO GET OPTIMUM PARAMETERS OF TURBULENCE CONSTANTS (cµ, c1, AND c2) OF COMPRESSIBLE FLUID DYNAMICS IN A CONFINED JET

This research aims to find the optimal standard k-e turbulence model constants (cµ, c1e, and c2e) for better predicting compressible fluid dynamics in an air jet ejector. The turbulence field in a jet flow plays an important role in influencing the performance of the momentum transfer process at a shear layer in nozzle application for momentum source and mixing process. In this research, some activities have been done before analyzing and optimizing the turbulence model constants, including preliminary turbulence modeling study for compressible flow in the air-jet ejector, verification, and validation with primary experimental data as well as by other secondary data. The preliminary studies in turbulence modeling presented that the turbulence modeling of a 3mm air jet-ejector resulted in a similar trend of the relation between entrainment ratio and motive fluid pressure. The results showed that the sensitive parameters in the standard k-emodel dissipation and diffusion terms, cµ, c1e, and c2e, strongly affected the optimum value of turbulence kinetic energy (k) and dissipation rate (e), compared to the reference model. Better k and e could be obtained by changing the c2e into positively proportional, but the cµ and c1e must be changed with opposite proportionality. It was found that the optimum standard k-e model constants in the case of air-jet ejector with 3 mm nozzle diameter for cµ, c1e, and c2e are 0.05, 1.48, and 1.88, respectively, with the error values for k being -8.88% and e being -17.44%.