Structural evolution of granular systems: theory

A general theory is developed for the evolution of the cell order (CO) distribution in planar granular systems. Dynamic equations are constructed and solved in closed form for several examples: systems under compression; dilation of very dense systems; and the general approach to steady state. We find that all the steady states are stable and that they satisfy a detailed balance-like condition when the CO$$\,\le 6$$ ≤ 6 . Illustrative numerical solutions of the evolution are shown. Our theoretical results are validated against an extensive simulation of a sheared system. The formalism can be readily extended to other structural characteristics, paving the way to a general theory of structural organisation of granular systems. Graphic abstract

CFD Assisted Steady-State Modelling of Restrictive Counterbalance Valves

The counterbalance valve is an important component in many hydraulic applications and its behaviour hugely impacts system stability and performance. Despite that, CBVs are rarely modelled accurately due to the effort required to obtain basic model parameters and the complexity involved in identifying expressions for flow forces and friction. This paper presents a CFD assisted approach to steady-state modelling of CBVs. It is applied to a 3-port restrictive commercially available counterbalance valve. The model obtained is based on detailed measurements of the valve geometry, a single data set and CFD modelling and includes flow forces and friction. The CFD assisted model is compared to experimental data at three temperatures and two versions of more classical steady-state model based on the orifice equation, uniform pressure distribution and experimental results. The results support the CFD assisted approach as a way to increase modelling accuracy. The load pressure corrected coulomb friction model used manages to capture the changes to hysteresis with temperature but not the changes with pilot pressure.

Stability Analysis of Cross Diffusion for the Walters B Fluid Model Saturated With Permeable Nanofluid

Stability analysis for the Walters-B model saturated with permeable nanofluid is taken under study including cross diffusion effects. The porous medium is defined using modified Darcy model, and the nanofluid is considered to have the impact of thermophoresis and Brownian motion. The thermal energy equation includes the effects of diffusion and also cross diffusion. For the study of linear theory, normal mode procedure is applied and to understand the nonlinear theory, the method of minimal representation of double Fourier series is utilized. The effects of nondimensional parameters such as concentration Rayleigh number, Lewis number, Soret and Dufour parameters, Solutal Rayleigh number, elastic parameter, Prandtl number, viscosity ratio, and conductivity ratio on the stationary and oscillatory convections are represented graphically. The effect of time on transient Nusselt numbers is also taken under investigation. It is concluded that when time is small, the three Nusselt numbers oscillate for all the governing parameters and approach to steady-state as time increases.

A new approach to steady state analysis of nonlinear electrical circuits

Purpose The purpose of this study is to identify a novel methodology for direct calculation of steady-state periodic solutions for electrical circuits described by nonlinear differential equations, in the time domain. Design/methodology/approach An iterative algorithm was created to determine periodic steady-state solutions for circuits with nonlinear elements in a chosen set of time instants. Findings This study found a novel differential operator for periodic functions and its application in the steady-state analysis. Research limitations/implications This approach can be extended to the determination of two- or multi-periodic solutions of nonlinear dynamic systems. Practical implications The complexity of the steady-state analysis can be reduced in comparison with the frequency-domain approach. Originality/value This study identified novel difference equations for direct steady-state analysis of nonlinear electrical circuits.