arXiv subjects

S. Kokou Dadzie

Publications and source records attributed to S. Kokou Dadzie.

8 recordsLinked to original sources

arXiv2024

Volume diffusion modelling of a sheared granular gas

Continuum fluid dynamic models based on the Navier-Stokes equations have previously been used to simulate granular media undergoing fluid-like shearing. These models, however, typically fail to predict the flow behaviour in confined environments as non-equilibrium particle effects dominate near walls. We adapt an extended hydrodynamic model for granular flows, which uses a density-gradient dependent ``volume diffusion'' term to correct the viscous stress tensor and heat flux, to simulate the shearing of a granular gas between two rough walls, and with corresponding boundary conditions. We use our volume diffusion model to predict channel flows for a range of mean volume fraction $\barϕ=0.01$--$0.4$, and inter-particle coefficients of restitution $e=0.8$ and $0.9$, and compare with Discrete Element Method (DEM) simulations and classical Navier-Stokes equations. Our model is capable of predicting non-uniform pressure, volume fraction and granular temperature, which become more significant for cases with mean volume fraction $\barϕ\sim0.1$, in which we typically observe non-uniform peak density variations, and large volume fraction gradients.

physics.flu-dyn↗

arXiv2021

Effects of Molecular Diffusivity on Shock Wave Structures in Monatomic Gases

We present a full investigation into shock wave profile description using hydrodynamics models. We identified constitutive equations that provide better agreement for all parameters involved in testing hydrodynamic equations for the prediction of shock structure in a monatomic gas in the Mach number range $1.0-11.0$. The constitutive equations are extracted from a previously derived thermomechanically consistent Burnett regime continuum flow model. The numerical computations of the resulting hydrodynamic equations along with classical ones are performed using a finite difference global solution (FDGS) scheme. Compared to previous studies that focussed mainly on the density profile across the shock, here we also include temperature profiles as well as non-negativity of entropy production throughout the shock. The results obtained show an improvement upon those obtained previously in the bi-velocity (or volume/mass diffusion) hydrodynamics and are more accurate than in the hydrodynamic models from expansions method solutions to the Boltzmann equation.

physics.flu-dyn↗

arXiv2020

Reinterpreting Shock Wave Structure Predictions using the Navier-Stokes Equations

Classical Navier-Stokes equations fail to predict shock wave profiles accurately. In this paper, the Navier-Stokes system is fully transformed using a velocity variable transformation. The transformed equations termed the re-casted Navier-Stokes equations display physics not initially included. We then analyse the stationary shock structure problem in a monatomic gas by solving both the classical and the re-casted Navier-Stokes equations numerically using a finite difference global solution (FDGS) scheme. The numerical results are presented for different upstream Mach numbers ranging from supersonic to hypersonic flows. We found that the re-casted Navier-Stokes equations show better agreements with the experimentally measured density and reciprocal shock thickness profiles.

physics.flu-dyn↗

arXiv2019

Recasting Navier-Stokes Equations

Classical Navier-Stokes equations fail to describe some flows in both the compressible and incompressible configurations. In this article, we propose a new methodology based on transforming the fluid mass velocity vector field to obtain a new class of continuum models. We uncover a class of continuum models which we call the re-casted Navier-Stokes. They naturally exhibit the physics of previously proposed models by different authors to substitute the original Navier-Stokes equations. The new models unlike the conventional Navier-Stokes appear as more complete forms of mass diffusion type continuum flow equations. They also form systematically a class of thermo-mechanically consistent hydrodynamic equations via the original equations. The plane wave analysis is performed to check their linear stability under small perturbations, which confirms that all re-casted models are spatially and temporally stable like their classical counterpart. We then use the Rayleigh-Brillouin scattering experiments to demonstrate that the re-casted equations may be better suited for explaining some of the experimental data where original Navier-Stokes fail.

physics.flu-dyn↗

arXiv2012

On the thermodynamics of volume/mass diffusion in fluids

In Physica A vol 387(24) (2008) pp6079-6094 [1], a kinetic equation for gas flows was proposed that leads to a set of four macroscopic conservation equations, rather than the traditional set of three equations. The additional equation arises due to local spatial random molecular behavior, which has been described as a volume or mass diffusion process. In this present paper, we describe a procedure to construct a Gibbs-type equation and a second-law associated with these kinetic and continuum models. We also point out the close link between the kinetic equation in [1] and that proposed previously by Klimontovich, and we discuss some of their compatibilities with classical mechanical principles. Finally, a dimensional analysis highlights the nature of volume/mass diffusion: it is a non-conventional diffusive process, with some similarities to the `ghost effect', which cannot be obtained from a fluid mechanical derivation that neglects non-local-equilibrium structures, as the conventional Navier-Stokes-Fourier model does.

math-ph↗

arXiv2009

A volume-based hydrodynamic approach to sound wave propagation in a monatomic gas

We investigate sound wave propagation in a monatomic gas using a volume-based hydrodynamic model. In Physica A vol 387(24) (2008) pp6079-6094, a microscopic volume-based kinetic approach was proposed by analyzing molecular spatial distributions; this led to a set of hydrodynamic equations incorporating a mass-density diffusion component. Here we find that these new mass-density diffusive flux and volume terms mean that our hydrodynamic model, uniquely, reproduces sound wave phase speed and damping measurements with excellent agreement over the full range of Knudsen number. In the high Knudsen number (high frequency) regime, our volume-based model predictions agree with the plane standing waves observed in the experiments, which existing kinetic and continuum models have great difficulty in capturing. In that regime, our results indicate that the "sound waves" presumed in the experiments may be better thought of as "mass-density waves", rather than the pressure waves of the continuum regime.

physics.flu-dyn↗

arXiv2006

A volume-based description of gas flows with localised mass-density variations

We reconsider some fundamental aspects of the fluid mechanics model, and the derivation of continuum flow equations from gas kinetic theory. Two topologies for fluid representation are presented, and a set of macroscopic equations are derived through a modified version of the classical Boltzmann kinetic equation for monatomic gases. The free volumes around the gaseous molecules are introduced into the set of kinetic microscopic parameters. Our new description comprises four, rather than three, conservation equations; the classical continuity equation, which conflates actual mass-density and number-density in a single equation, has been split into a conservation equation of mass (which involves only the classical number-density of the gaseous particles) and an evolution equation purely of the mass-density (mass divided by the actual volume of the fluid). We propose this model as a better description of gas flows displaying non-local-thermodynamic-equilibrium (rarefied flows), flows with relatively large variations of macroscopic properties, and/or highly compressible fluids/flows.

physics.flu-dyn↗

arXiv2006

A constitutive model for volume-based descriptions of gas flows

We derive the pressure tensor and the heat flux to accompany the new macroscopic conservation equations that we developed previously in a volume-based kinetic framework for gas flows. This kinetic description allows for expansion or compression of a fluid element, and is characterized by a flux of volume that conventional modelling does not account for. A new convective form of transport arises from this new approach, which is due purely to macroscopic expansion or compression. It supplements the conventional transport processes, which are transport due purely to mass motion (classical convective transport) and transport due purely to random motion (diffusive transport). In addition, we show that the thermodynamic parameters of the fluid (temperature and pressure) appear with new non-equilibrium contributions that depend on density variations in the gas. Our new model may be useful for describing gas flows that display non-local-thermodynamic-equilibrium (rarefied gas flows), flows with relatively large variations of macroscopic properties, and/or highly compressible fluids and flows.

physics.flu-dyn↗