Fractal Analysis of a Non-Newtonian Fluid Flow in a Rough-Walled Pipe

Bouchendouka, Abdellah; Fellah, Zine El Abiddine; Larbi, Zakaria; Louna, Zineeddine; Ogam, Erick; Fellah, M.; Dépollier, Claude

doi:10.3390/ma15103700

Cited by 6 publications

(5 citation statements)

References 66 publications

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“…This advancement in generalizing differential vector operators to non-integer dimensions supports the use of continuous models for fractal media in NIDS [13,14]. The NIDS calculus developed from this allows for the description of both isotropic and anisotropic fractal media, and has been instrumental in advancing the study of fractal hydrodynamics [15,16,17,18,19], fractal electrodynamics, the elasticity of fractal materials, and acoustics of fractal porous media [20,21,22]. This study aims to apply the NIDS operators referenced in prior research to model ultrasonic wave propagation through a fractal porous medium.…”

Section: Introductionmentioning

confidence: 83%

Non-Integer Dimensional Analysis of Ultrasonic Wave Propagation in Fractal Porous Media

Bouchendouka,

Fellah,

Ogam

et al. 2024

J. Phys.: Conf. Ser.

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This paper explores the acoustics of porous media characterized by fractal, or self-similar, structures. Employing a fractal approach, we use differential operators in non-integer dimensional spaces to address the fundamental equations of acoustics in such media. The primary aim is to examine the transmission of ultrasonic waves within a fractal porous medium. Our findings reveal that the fractal dimension significantly influences wave transmission. In fractal porous materials, waves travel along more complex and intricate paths, resulting in increased tortuosity and attenuation. We introduce the concept of an effective path length leff , which is dependent on the fractal dimension Dx , to describe the actual trajectory of wave propagation. Additionally, we define an effective tortuosity αDx , directly proportional to l e f f 2 , to quantify the additional tortuosity brought about by the fractal structure. The insights gained from this study are crucial, as they enhance our understanding of wave behavior in self-similar porous media, which are prevalent in various natural settings and have multiple practical applications, including sound insulation and the design of acoustic materials. Furthermore, understanding the impact of fractal dimensions on wave behavior is vital for developing more efficient acoustic solutions. This research also sets the stage for further theoretical and experimental work on applying fractal geometry to analyze wave propagation in porous structures.

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Section: Introductionmentioning

confidence: 83%

Non-Integer Dimensional Analysis of Ultrasonic Wave Propagation in Fractal Porous Media

Bouchendouka,

Fellah,

Ogam

et al. 2024

J. Phys.: Conf. Ser.

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“…In acoustics, fractals have been used to model the propagation of sound in complex and heterogeneous media such as porous materials [5,6] and granular media, and to analyze complex acoustic signals such as cardiac and vocal signals. In non-destructive testing, fractals have been used to detect defects in materials such as cracks, inclusions, and porosities, and to measure surface properties of materials, such as roughness [7] and texture, using fractal-based image processing techniques.…”

Section: Introductionmentioning

confidence: 99%

Ultrasonic Propagation in Fractal Porous Material Having Rigid Frame

Fellah,

Bouchendouka,

Martin

et al. 2023

10th ECCOMAS Thematic Conference on Smart Structures and Materials

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This paper discusses the impact of the fractal structure of porous materials on wave behavior. In addition to commonly used parameters such as porosity, tortuosity, viscous and thermal characteristic lengths, a fractal dimension (α) can be introduced to represent the selfsimilarity of the material. The Helmholtz equation for wave propagation in a porous medium can then be modified to depend on non-integer dimensions. The fractal structure affects the wave's speed, attenuation, and phase shifts, with supersonic wave speeds possible for for certain values of the fractal dimension. The equivalent thickness of the material also varies with the fractal dimension becoming larger for low values of the fractal dimension. This provides us with valuable insights into the potential for creating novel metamaterials with exceptional acoustic properties by adjusting the fractal dimension value, enabling the attainment of supersonic velocities and substantial equivalent thicknesses. Understanding the effect of the fractal dimension on wave behavior has important implications for developing effective acoustic materials and can inform research in noise reduction, metamaterials, medicine, seismology, geophysics, and petroleum engineering.

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“…The results showed the effect of the self-similar structure on the rheological behavior of the non-Newtonian fluid [43]. Another study [44] looked at the impact of surface roughness on the flow of a viscous non-Newtonian fluid, using surface fractal dimensions to model the roughness. In this paper, a generalization of the flow of a self-similar Newtonian fluid through a rough-walled pipe is presented.…”

Section: Introductionmentioning

confidence: 99%

A Generalization of Poiseuille’s Law for the Flow of a Self-Similar (Fractal) Fluid through a Tube Having a Fractal Rough Surface

et al. 2023

Self Cite

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In this paper, a generalization of Poiseuille’s law for a self-similar fluid flow through a tube having a rough surface is proposed. The originality of this work is to consider, simultaneously, the self-similarity structure of the fluid and the roughness of the tube surface. This study can have a wide range of applications, for example, for fractal fluid dynamics in hydrology. The roughness of the tube surface presents a fractal structure that can be described by the surface fractal noninteger dimensions. Complex fluids that are invariant to changes in scale (self-similar) are modeled as a continuous medium in noninteger dimensional spaces. In this work, the analytical solution of the Navier–Stokes equations for the case of a self-similar fluid flow through a rough “fractal” tube is presented. New expressions of the velocity profiles, the fluid discharge, and the friction factor are determined analytically and plotted numerically. These expressions contain fractal dimensions describing the effects of the fractal aspect of the fluid and of that of the tube surface. This approach reveals some very important results. For the velocity profile to represent a physical solution, the fractal dimension of the fluid ranges between 0.5 and 1. This study also qualitatively demonstrates that self-similar fluids have shear thickening-like behavior. The fractal (self-similarity) nature of the fluid and the roughness of the surface both have a huge impact on the dynamics of the flow. The fractal dimension of the fluid affects the amplitude and the shape of the velocity profile, which loses its parabolic shape for some values of the fluid fractal dimension. By contrast, the roughness of the surface affects only the amplitude of the velocity profile. Nevertheless, both the fluid’s fractal dimension and the surface roughness have a major influence on the behavior of the fluid, and should not be neglected.

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Fractal Analysis of a Non-Newtonian Fluid Flow in a Rough-Walled Pipe

Cited by 6 publications

References 66 publications

Non-Integer Dimensional Analysis of Ultrasonic Wave Propagation in Fractal Porous Media

Non-Integer Dimensional Analysis of Ultrasonic Wave Propagation in Fractal Porous Media

Ultrasonic Propagation in Fractal Porous Material Having Rigid Frame

A Generalization of Poiseuille’s Law for the Flow of a Self-Similar (Fractal) Fluid through a Tube Having a Fractal Rough Surface

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