Bulk viscosity of dilute monatomic gases revisited

Sharma, Bhanuday; Pareek, Savitha; Kumar, Rakesh

doi:10.1016/j.euromechflu.2022.10.009

Cited by 6 publications

(5 citation statements)

References 43 publications

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“…In the literature, it is said that bulk viscosity of monatomic gases is zero, since bulk viscosity is linked to the distribution of energy within the different modes motion and that the monatomic gases have only translational mode. However, Sharma et al [10] tell that, although the mechanisms for the distribution of energy within a molecule are absent for the monatomic gases, the arrangement of the atoms themselves also demand time. The reason for the widespread view of zero bulk viscosity for monatomic gases is reported to be due to the fact that the numbers are five orders of magnitude less than those for molecular gases.…”

Section: Resultsmentioning

confidence: 99%

“…According to widely accepted view based on this paradigm, only the monatomic gases are devoid of bulk viscosity. However, even that assumption has been shown to be a "good enough" approximation [10], because even if the particles are monatomic, their distribution over space and the distribution of energy on them takes time to achieve equilibrium after an interaction. However, this effect that is manifest on the monatomic particles is several orders of magnitude smaller than that observed on the distribution of energy within the nonmonatomic particles over different modes of motion.…”

Section: Introductionmentioning

confidence: 99%

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Reconciliation of Thermodynamic and Mechanical Pressures and Development of a Frequency-Based Formula for Speed of Sound in Gases

Ogretim

2023

Preprint

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Discrepancy of the thermodynamic and mechanical pressures is a problem at the heart of the current theory of fluid mechanics. The fluid property that leads to this situation is the bulk viscosity, whose effects are zero for incompressible cases and are negligible for most other applications. Therefore, this discrepancy is conventionally ignored in phenomena other than acoustics and shock related ones. However, the flaw in the theory still persists since the late 19th century. In the present study, to improve the existing theory and to come up with a consistent structure in terms of mechanical and thermodynamic pressures, a novel fluid element model is proposed. Unlike the current fluid model that assumes a continuum of fluid, the present model proposes fluid elements that are separated from each other by a thin energy field that manifests itself as the mechanical pressure. Also, unlike the current efforts in explaining bulk viscosity effects through atomic level dynamics, the present model proposes a mesoscale analysis where bulk viscosity is integrated into the fluid element as a damper. Considering all these new features, each fluid element in this new model contains energy in both the wave form and the particle form. Of these two, wave energy is the cause of the thermodynamic pressure. In this manuscript, first, justifications of the mentioned aspects of the new fluid model are given. Then, a speed of sound expression is derived based on the new model involving the bulk viscosity effects. Resultant expression is, then, used for comparison with the findings of previous studies. The proposed formula can also be used to calculate the bulk viscosity of gases at different acoustic frequencies in a way that is more direct than those currently in use.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reconciliation of Thermodynamic and Mechanical Pressures and Development of a Frequency-Based Formula for Speed of Sound in Gases

Ogretim

2023

Preprint

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“…In light of the research conducted by Sharma (2023) [15], it has been demonstrated that the impact of bulk viscosity for Argon monoatomic gas is negligible. Consequently, throughout this work, the value for bulk viscosity has been assumed to be zero.…”

Section: Simplified Isotropic Modelmentioning

confidence: 97%

Physics-constrained deep learning-based model for non-equilibrium flows

Monti,

Singh,

Sirignano

et al. 2024

AIAA SCITECH 2024 Forum

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The construction of accurate and computationally affordable computer models for simulating non-equilibrium fluid flows is a challenging task, particularly when dealing with hypersonic applications. The popular Navier-Stokes (NS) model yields unreliable predictions whenever the continuum assumption fails (approx. for a Knudsen number Kn > 0.1). On the other hand, the large computational cost entailed in solving the more suited Boltzmann equation makes its numerical solution impossible for non-trivial cases. In such cases, even the most efficient Direct-Simulation Monte Carlo (DSMC) solution methods may result prohibitively expensive, in particular if approx. Kn < 10 and if thermochemical nonequilibrium is considered.This paper focuses on improving the computational capabilities for predicting nonequilibrium hypersonic flows in the transitional regime 0.1 < Kn < 10. Namely, we build physics-constrained Deep Learning (DL) augmentation terms that take advantage of the known and resolvable physics e.g., first principles, thermodynamics laws, and conservation laws, and exploit them to improve the accuracy of the NS solution. The aim is to achieve a prediction accuracy comparable to that of the DSMC solution while maintaining a computational cost comparable to solving the standard NS equations.Previous studies employed Deep Neural Networks (DNNs) for enhancing the modeling of incompressible fluid flows, with particular reference to turbulent phenomena, but their potential has not been fully deployed for hypersonic applications, for which literature concerning DL-DNNs augmentation models is still scarce. Recent research by Sirignano et al. [1] proposed an innovative online training strategy that leverages the adjoint method to optimize the parameters of a DL model by solving a constrained PDE. This approach allows consistent mathematical-physical training and was successfully applied to hypersonic problems by Nair et al. [2] for a 1D shock flow in the transitional regime. However, this model does not embed the first principle of physics, making it case-dependent and preventing its extension to general 2D/3D applications.The present work aims to overcome these issues and extend the state-of-the-art by proposing a flexible framework for building physics-constrained neural network closures of general application. To overcome these drawbacks, the pursued approach is based on the premise that physical laws and constraints are inherently embedded in real applications and they can be exploited to guide the development of more robust and accurate closures. By incorporating these constraints into the training process, we aim to develop a model that can capture both the universal physics, which is general, and the physics encoded in the data, which is case-dependent. It is important to note that the main advantage of the approach proposed in this work, compared to other alternative approaches, is its ability to generalize: the structure of the developed model is case-independent and permits the use of the same model on very differ...

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“…This mechanism of bulk viscosity is present in all fluids including monatomic gases. Hence, monatomic gases at atmospheric conditions have a small (O(10 −10 ) Pa s) [49] but non-zero bulk viscosity. It should also be noted that at hypothetical dilute gas conditions, the bulk viscosity of monatomic gases is considered to be absolute zero.…”

Section: Intrinsic Bulk Viscositymentioning

confidence: 99%

A brief introduction to bulk viscosity of fluids

Sharma¹,

Kumar²

2023

Preprint

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Fluid flows are typically studied by solving the Navier-Stokes equation. One of the fundamental assumptions of this equation is Stokes' hypothesis. This hypothesis assumes bulk viscosity, µ b , to be identically zero. The Stokes' hypothesis is a reasonable approximation for commonly observed fluid flows; therefore, Navier-Stokes equation gives satisfactory results in these situations. However, there are circumstances where this hypothesis does not hold good, and therefore, the classical Navier-Stokes equation becomes inapt. These situations include the absorption of sound waves, hypersonic flows, turbulent flows, and flow of Martian air etc. Reliable analytical and computational studies of these flows requires account of bulk viscosity in the governing equations. In this article, we provide a brief review of the subject of bulk viscosity. We start with a brief background of this topic. Then we discuss the underlying microscopic mechanisms that give rise to bulk viscosity effects. It was followed by a review of methods available in the literature for estimation of this parameter. Finally, a review of the studies that analyze the effects of bulk viscosity in various fluid flows is provided.

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Bulk viscosity of dilute monatomic gases revisited

Cited by 6 publications

References 43 publications

Reconciliation of Thermodynamic and Mechanical Pressures and Development of a Frequency-Based Formula for Speed of Sound in Gases

Reconciliation of Thermodynamic and Mechanical Pressures and Development of a Frequency-Based Formula for Speed of Sound in Gases

Physics-constrained deep learning-based model for non-equilibrium flows

A brief introduction to bulk viscosity of fluids

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