Navier–Stokes Equations and Bulk Viscosity for a Polyatomic Gas with Temperature-Dependent Specific Heats

Kosuge, Shingo; Aoki, Kazuo

doi:10.3390/fluids8010005

Cited by 6 publications

(1 citation statement)

References 61 publications

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“…However, Kustova, Mekhonoshina & Kosareva (2019) proposed a new bulk viscosity theory using the Chapman-Enskog method, which suggests that the CO 2 bulk viscosity and shear viscosity coefficients are of the same order at room temperature. In addition, many researchers have developed different theoretical models that include temperature-dependent bulk viscosity in recent years, such as the variable specific heat two-temperature Navier-Stokes equation (Kosuge & Aoki 2022), a state-to-state model suitable for mixtures of gases (Bruno & Giovangigli 2022), and a kinetic model with temperature-dependent vibrational degrees of freedom (Li & Wu 2022). Despite the many methods of evaluating the bulk viscosity coefficients, there are still large uncertainties in the bulk viscosity coefficients of common gases such as air, N 2 and CO 2 (Graves & Argrow 1999;Vieitez et al 2010;Jaeger, Matar & Müller 2018;.…”

Section: Casementioning

confidence: 99%

Effect of bulk viscosity on the hypersonic compressible turbulent boundary layer

Zheng,

Feng,

Zheng

2024

J. Fluid Mech.

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The impact of bulk viscosity is unclear with considering the increased dilatational dissipation and compressibility effects in hypersonic turbulence flows. In this study, we employ direct numerical simulations to conduct comprehensive analysis of the effect of bulk viscosity on hypersonic turbulent boundary layer flow over a flat plate. The results demonstrate that the scaling relations remain valid even when accounting for large bulk viscosity. However, the wall-normal velocity fluctuations $v_{rms}^{\prime \prime }$ decrease significantly in the viscous sublayer due to the enhanced bulk dilatational dissipation. The intensity of travelling-wave-like alternating positive and negative structures of instantaneous pressure fluctuations $p_{rms}^{\prime }$ in the near-wall region decreases distinctly after considering the bulk viscosity, which is attributed mainly to the reduction of compressible pressure fluctuations $p_{c,rms}^{+}$ . Furthermore, the velocity divergence $\partial u_{i} / \partial x_{i}$ undergoes a significant decrease by bulk viscosity. In short, our results indicate that bulk viscosity can weaken the compressibility of the hypersonic turbulent boundary layer and becomes more significant as the Mach number increases and the wall temperature decreases. Notably, when the bulk-to-shear viscosity ratio of the gas reaches a few hundred levels ( $\mu _b/\mu =O(10^2)$ ), and mechanical behaviour of the near-wall region ( $\kern 0.06em y^+\le 30$ ) is of greater interest, the impact of bulk viscosity on the hypersonic cold-wall turbulent boundary layer may not be negligible.

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Section: Casementioning

confidence: 99%

Effect of bulk viscosity on the hypersonic compressible turbulent boundary layer

Zheng,

Feng,

Zheng

2024

J. Fluid Mech.

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Capturing non-equilibrium in hypersonic flows: Insights from a two-temperature model in polyatomic rarefied gases

Kumar,

Rana

2024

Physics of Fluids

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The study utilizes a two-temperature model to analyze non-equilibrium in normal shocks within hypersonic flows in polyatomic rarefied gases. Derived from the extended second law of thermodynamics, this model separates translational and internal temperatures in polyatomic gases, providing a more accurate depiction of non-equilibrium gas flow compared to classical theories like the Navier–Stokes and Fourier (NSF) system. Notably, the analysis reveals that the two-temperature model incorporates an additional contribution to the heat flux due to the gradient of the dynamic temperature, resulting in improved accuracy, especially for high Mach numbers. Results show that the model gives satisfactory shock density and temperature profiles up to Mach 10, with very good agreement observed up to Mach 6.1 compared to the classical NSF model. We conduct an order of magnitude analysis on the dynamic temperature and heat flux gradients appearing in the new constitutive equation using the Mott-Smith method. This analysis highlights the impact of these terms on accurately modeling polyatomic gas behavior in high-speed flows. The effects of bulk viscosity and incoming temperature on shock profiles are also investigated, contributing to a better understanding of shock wave structures in polyatomic gases and their implications for hypersonic flow dynamics.

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Scientific School of Nonequilibrium Aeromechanics at St. Petersburg State University

Voroshilova,

Istomin,

Kunova

et al. 2023

Vestnik St.Petersb. Univ.Math.

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Navier–Stokes Equations and Bulk Viscosity for a Polyatomic Gas with Temperature-Dependent Specific Heats

Cited by 6 publications

References 61 publications

Effect of bulk viscosity on the hypersonic compressible turbulent boundary layer

Effect of bulk viscosity on the hypersonic compressible turbulent boundary layer

Capturing non-equilibrium in hypersonic flows: Insights from a two-temperature model in polyatomic rarefied gases

Scientific School of Nonequilibrium Aeromechanics at St. Petersburg State University

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