A major limitation of the weakly compressible approaches to simulate incompressible flows is the appearance of artificial acoustic waves that introduce a large mass conservation error and lead to spurious oscillations in the force coefficients. In this work, we propose a non-homogeneous anisotropic bulk viscosity term to effectively damp the acoustic waves. By implementing this term in a computational framework based on the recently proposed general pressure equation, we demonstrate that the non-homogeneous and anisotropic nature of the term makes it significantly more effective than the isotropic homogeneous version widely used in the literature. Moreover, it is computationally more efficient than the pressure (or mass) diffusion term, which is an alternative mechanism used to suppress acoustic waves. We simulate a range of benchmark problems to comprehensively investigate the performance of the bulk viscosity on the effective suppression of acoustic waves, mass conservation error, order of convergence of the solver, and computational efficiency. The proposed form of the bulk viscosity enables fairly accurate modelling of the initial transients of unsteady simulations, which is highly challenging for weakly compressible approaches, and to the best of our knowledge, existing approaches can't provide an accurate prediction of such transients.
Acoustic wave attenuation due to vibrational and rotational molecular relaxation, under simplifying assumptions of near-thermodynamic equilibrium and absence of molecular dissociations, can be accounted for by specifying a bulk viscosity coefficient $μ_B$. In this paper, we propose a simple frequency-dependent bulk viscosity model which, under such assumptions, accurately captures wave attenuation rates from infrasonic to ultrasonic frequencies in Navier--Stokes and lattice Boltzmann simulations. The proposed model can be extended to any gas mixture for which molecular relaxation timescales an…
Hydrodynamic flow field and frictional resistance coefficient of a disk rotating steadily in a compressible fluid layer with odd viscosity on a rigid substrate
The Open University（开放大学）；Max Planck Institute for Dynamics and Self-Organization（马克斯·普朗克动力学与自组织研究所）
Analytical response functions for a compressible thin fluid layer with odd viscosity
The Open University（开放大学）；Max Planck Institute for Dynamics and Self-Organization (MPI–DS)（马克斯·普朗克动力学与自组织研究所）；Kyoto University（京都大学）；Wenzhou Institute, University of Chinese Academy of Sciences（中国科学院大学温州研究院）
A new exact solution of the Navier-Stokes equation is derived for the compressible flows which are far from equilibrium in the limit of extremely low shear viscosity and relatively large volume viscosity. The closed description of the evolution of statistical moments of velocity is obtained, thereby bypassing the closure problem in the theory of turbulence.
In this paper, we perform analysis of the fluid velocity vector field divergence $\nabla \cdot \vec{u}$ derived from the continuity equation, and we explore its application in the Navier-Stokes equations for compressible fluids $ρ(\vec{x},t)\ne const$, occupying all of $\vec{x}\in R^{3} $ space at any $t\geq 0$. The resulting velocity vector field divergence $\nabla \cdot \vec{u}=-\frac{1}{ρ} (\frac{\partial ρ}{\partial t} +\vec{u}\cdot \nabla ρ)$ is a direct consequence of the fluid density rate of change over time $\frac{\partial ρ}{\partial t}$ and over space $\nabla ρ$, in addition to the …
When an acoustic wave travels in a lossy medium such as a liquid, it progressively transfers its pseudo-momentum to the fluid, which results in a steady acoustic streaming. Remarkably, the phenomenon involves a balance between sound attenuation and shear, such that viscosity vanishes in the final expression of the velocity field. For this reason, the effect of viscosity has long been ignored in acoustic streaming experiments. Here, we show experimentally that the viscosity plays a major role in cavities such as the streaming induced by surface acoustic waves in sessile droplets. We develop a n…
High-amplitude free stream turbulence and surface roughness elements can excite a laminar boundary layer flow sufficiently to cause streamwise oriented vortices to develop. These vortices resemble elongated streaks having alternate spanwise variations of the streamwise velocity. Downstream, the vortices `wobble' through an inviscid secondary instability mechanism and, ultimately, transition to turbulence. We formulate an optimal control algorithm to suppress the growth rate of the streamwise vortex system. Considering a high Reynolds number asymptotic framework, we reduce the full compressible…
The effects of density and viscosity fluctuations on the total stress balance are identified and used to create a new mean velocity transformation for compressible boundary layers. This work is enabled by an extensive database of direct numerical simulations that incorporate wall-cooling, semi-local Reynolds numbers ranging from 800 to 34000, and Mach numbers up to 12. The role, significance and physical mechanisms connecting density and viscosity fluctuations to the momentum balance and to the viscous, turbulent and total stresses are presented,allowing the creation of generalized formulation…
We are concerned with the global existence theory for spherically symmetric solutions of the multidimensional compressible Euler equations with large initial data of positive far-field density. The central feature of the solutions is the strengthening of waves as they move radially inward toward the origin. Various examples have shown that the spherically symmetric solutions of the Euler equations blow up near the origin at certain time. A fundamental unsolved problem is whether the density of the global solution would form concentration to become a measure near the origin for the case when th…
We consider an isotropic compressible non-dissipative fluid with broken parity subject to free surface boundary conditions in two spatial dimensions. The hydrodynamic equations describing the bulk dynamics of the fluid as well as the free surface boundary conditions depend explicitly on the parity breaking non-dissipative odd viscosity term. We construct a variational principle in the form of an effective action which gives both bulk hydrodynamic equations and free surface boundary conditions. The free surface boundary conditions require an additional boundary term in the action which resemble…
The ability of viscous layer models to describe the attenuation of waves propagating in grease-pancake ice covered ocean is investigated. In particular, the Keller's model Keller [1998], the two-layer viscous model [De Carolis and Desiderio 2002] and the close-packing model [De Santi and Olla 2017] are extensively validated by using wave attenuation data collected during two different field campaigns (Weddell Sea, Antarctica, April 2000; western Arctic Ocean, autumn 2015). We use these data to validate the three models by minimizing the differences between the measured and model wave attenuati…
