Diffusive Bejan number and second law of thermodynamics toward a new dimensionless formulation of fluid dynamics laws

In a recent paper, Liversage and Trancossi have defined a new formulation of drag as a function of the dimensionless Bejan and Reynolds numbers. Further analysis of this hypothesis has permitted to obtain a new dimensionless formulation of the fundamental equations of fluid dynamics in their integral form. The resulting equations have been deeply discussed for the thermodynamic definition of Bejan number evidencing that the proposed formulation allows solving fluid dynamic problems in terms of entropy generation, allowing an effective optimization of design in terms of the Second law of thermodynamics. Some samples are discussed evidencing how the new formulation can support the generation of an optimized configuration of fluidic devices and that the optimized configurations allow minimizing the entropy generation.

Dimensionless formulation for human stability in open flows

ABSTRACT The stability of humans partially immersed in risky open water flows, resulting from urban flooding caused for example by dam breaks, or failures in drainage systems, or natural extreme events, is a topic of increasing interest because it involves the human safety in an environment that is more and more subjected to extreme events of hydraulic nature. The studies in this field of the applied fluid mechanics generally present equations that handle the results through dimensional quantities. These results were generally obtained in specific experiments for the evaluation of the stability of models of the human body. Intending to advance in the direction of a more general formulation, a dimensional analysis for the problem of human stability in open flows is presented here, showing dimensionless groups that represent the mentioned problem. Equations using these nondimensional groups were then developed using statistical analyses and approximations based on principles of physics and on data of the human body. The results obtained with the proposed methodology are of very good quality, presenting high correlation coefficients and good agreement between measured and calculated data.

Influence of viscosity contrast on buoyantly unstable miscible fluids in porous media

The influence of viscosity contrast on buoyantly unstable miscible fluids in a porous medium is investigated through a linear stability analysis (LSA) as well as direct numerical simulations (DNS). The linear stability method implemented in this paper is based on an initial value approach, which helps to capture the onset of instability more accurately than the quasi-steady-state analysis. In the absence of displacement, we show that viscosity contrast delays the onset of instability in buoyantly unstable miscible fluids. Further, it is observed that by suitably choosing the viscosity contrast and injection velocity a gravitationally unstable miscible interface can be stabilized completely. Through LSA we draw a phase diagram, which shows three distinct stability regions in a parameter space spanned by the displacement velocity and the viscosity contrast. DNS are performed corresponding to parameters from each regime and the results obtained are in accordance with the linear stability results. Moreover, the conversion from one dimensionless formulation to another and its importance when comparing the different type of flow problem associated with each dimensionless formulation are discussed. We also calculate${\it\epsilon}$-pseudo-spectra of the time dependent linearized operator to investigate the response to external excitation.

Low Cost Experimental Vibration Analysis of a Cantilever Beam Under Base Excitation

This paper presents the investigation of operational deflection shapes of vibration of a cantilever beam using a low-cost digital video camera, and by application of image processing techniques. The beam is uniform and under base excitation. The analytical model of the system is developed using dimensionless formulation. The analytical ODS’s are derived, and then compared with those found from experiment. The significance of this research is that it provides the researchers an inexpensive alternative tool for investigating the behavior of systems with low-frequency dynamics.