Elementary scales and the lack of Fourier paradox for Fourier fluids

Nucci, Carmine Di; Celli, Daniele; Fischione, Piera; Pasquali, Davide

doi:10.1007/s11012-021-01444-x

Cited by 4 publications

(6 citation statements)

References 8 publications

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“…Within the framework of CCT, the ESM [18,20] allows us to define the elementary spatial scale |dr| and the elementary time scale |dt| such that:…”

Section: Elementary Scales Methods (Esm)mentioning

confidence: 99%

“…After some brief remarks on the simple isotropic linear viscous fluid (Section 2), we show the connection between the closure equation for the turbulent bulk viscosity and the elementary time scale. For this purpose, Section 3 recalls the main features of the Elementary Scales Method (ESM) [18]. In Section 4, we suggest a dimensionless formulation of the field equations.…”

Section: Introductionmentioning

confidence: 99%

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New Dimensionless Number for the Transition from Viscous to Turbulent Flow

Nucci

Celli

Pasquali

et al. 2022

Fluids

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Within the framework of Classical Continuum Thermomechanics, we consider an unsteady isothermal flow of a simple isotropic linear viscous fluid in the liquid state to investigate the transient flow conditions. Despite the attention paid to this problem by several research works, it seems that the understanding of turbulence in these flow conditions is controversial. We propose a dimensionless procedure that highlights some aspects related to the transition from viscous to turbulent flow which occurs when a finite amplitude pressure wave travels through the fluid. This kind of transition is demonstrated to be described by a (first) dimensionless number, which involves the bulk viscosity. Furthermore, in the turbulent flow regime, we show the role played by a (second) dimensionless number, which involves the turbulent bulk viscosity, in entropy production. Within the frame of the 1D model, we test the performance of the dimensionless procedure using experimental data on the pressure waves propagation in a long pipe (water hammer phenomenon). The obtained numerical results show good agreement with the experimental data. The results’ inspection confirms the predominant role of the turbulent bulk viscosity on energy dissipation processes.

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“…Within the framework of CCT, the ESM [18,20] allows us to define the elementary spatial scale |dr| and the elementary time scale |dt| such that:…”

Section: Elementary Scales Methods (Esm)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

New Dimensionless Number for the Transition from Viscous to Turbulent Flow

Nucci

Celli

Pasquali

et al. 2022

Fluids

Self Cite

View full text Add to dashboard Cite

show abstract

“…Within the framework of the continuum model, the above procedure is exact (without approximations). On the other hand, the continuity equation can be deduced using a second approach [3,10]. Setting…”

Section: Continuity Equationmentioning

confidence: 99%

“…where t r is the relaxation time, i.e., the time it takes to restore a local thermodynamic equilibrium (LTE) condition from a local thermodynamic non-equilibrium condition, |dt| the elementary time scale [3]. For long relaxation time and/or for short elementary time scale, the LTE is invalid, and t r |dt| ∼ 1.…”

Section: Introductionmentioning

confidence: 99%

“…It should be stressed that the study approach based on the elementary scales allows to extend and refine the range of applicability of the classical irreversible thermodynamics. In [7], the elementary time scale is used to define a turbulence model able to describe the energy dissipation in shock waves; in [3] a method based on the elementary scales is employed to remove the heat conduction paradox concerning the infinite speed of signal diffusion in the Fourier theory (Fourier paradox). The choice of the elementary time scale |dt| is not arbitrary.…”

Section: Introductionmentioning

confidence: 99%

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Archives of Thermodynamics

2022

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This brief note focuses on a simple fluid, i.e., a homogeneous, chemically inert, and electrically neutral fluid, for which, in the linear nonequilibrium regime, the thermodynamic state is expressed by a relation between pressure, temperature, and density. The approach based on the elementary scales is used to check the validity range of both the classical irreversible thermodynamics and the extended irreversible thermodynamics. The achieved result reveals that the classical irreversible thermodynamics fails in providing an adequate response when the mechanical solicitations exceed limit values.

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Decomposition of the mechanical stress tensor: from the compressible Navier–Stokes equation to a turbulent potential flow model

Di Nucci,

Michele,

Di Risio

2024

Acta Mech

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We frame the mechanical stress tensor decomposition in a general procedure which involves the Helmholtz–Hodge decomposition. We highlight the impact of the mechanical stress tensor decomposition on the Navier–Stokes equation, with emphasis on the dissipation function. For fluids with low compressibility, we draw some insights on the Reynolds Averaged Navier–Stokes equations, and on the Reynolds stress tensor decomposition. We derive a turbulent potential flow model, and investigate the transition from viscous potential flow to turbulent potential flow. Under low Mach number approximation, we apply the turbulent potential flow model to one-dimensional propagation of large amplitude pressure waves in liquid-filled pipe.

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Elementary scales and the lack of Fourier paradox for Fourier fluids

Cited by 4 publications

References 8 publications

New Dimensionless Number for the Transition from Viscous to Turbulent Flow

New Dimensionless Number for the Transition from Viscous to Turbulent Flow

Archives of Thermodynamics

Decomposition of the mechanical stress tensor: from the compressible Navier–Stokes equation to a turbulent potential flow model

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