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Velocity gradient

About: Velocity gradient is a research topic. Over the lifetime, 3013 publications have been published within this topic receiving 77120 citations.


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TL;DR: In this paper, the authors used numerical simulations to describe a transport bifurcation in a differentially rotating tokamak plasma, where heat is transported almost neoclassically, while momentum transport is dominated by subcritical PVG turbulence.
Abstract: First-principles numerical simulations are used to describe a transport bifurcation in a differentially rotating tokamak plasma. Such a bifurcation is more probable in a region of zero magnetic shear than one of finite magnetic shear because in the former case the component of the sheared toroidal flow that is perpendicular to the magnetic field has the strongest suppressing effect on the turbulence. In the zero-magnetic-shear regime, there are no growing linear eigenmodes at any finite value of flow shear. However, subcritical turbulence can be sustained, owing to the transient growth of modes driven by the ion temperature gradient (ITG) and the parallel velocity gradient (PVG). Nonetheless, in a parameter space containing a wide range of temperature gradients and velocity shears, there is a sizeable window where all turbulence is suppressed. Combined with the relatively low transport of momentum by collisional (neoclassical) mechanisms, this produces the conditions for a bifurcation from low to high temperature and velocity gradients. The path of this bifurcation is mapped out using interpolation from a large number of simulations. Numerical simulations are also used to construct a parametric model which accurately describes the combined effect of the temperature gradient and the flow gradient over a wide range of their values. Using this parametric model, it is shown that in this reduced-transport state, heat is transported almost neoclassically, while momentum transport is dominated by subcritical PVG turbulence. It is further shown that for any given input of torque, there is an optimum input of heat which maximises the temperature gradient. The parametric model describes both the behaviour of the subcritical turbulence and the complicated effect of the flow shear on the transport stiffness. It may prove useful for transport modelling of tokamaks with sheared flows.

20 citations

Journal ArticleDOI
TL;DR: In this article, the authors show that the suspension shear-thickens due to elastic stretching in strain hot spots near the particle, despite the fact that the stress inside the particles decreases relative to the Newtonian case.
Abstract: We give the first correction to the suspension viscosity due to fluid elasticity for a dilute suspension of spheres in a viscoelastic medium. Our perturbation theory is valid to $O(\phi\mathrm{Wi}^2)$ in the Weissenberg number $\mathrm{Wi}=\dot\gamma \lambda$, where $\dot\gamma$ is the typical magnitude of the suspension velocity gradient, and $\lambda$ is the relaxation time of the viscoelastic fluid. For shear flow we find that the suspension shear-thickens due to elastic stretching in strain hot spots near the particle, despite the fact that the stress inside the particles decreases relative to the Newtonian case. We thus argue that it is crucial to correctly model the extensional rheology of the suspending medium to predict the shear rheology of the suspension. For uniaxial extensional flow we correct existing results at $O(\phi\mathrm{Wi})$, and find dramatic strain-rate thickening at $O(\phi\mathrm{Wi}^2)$. We validate our theory with fully resolved numerical simulations.

20 citations

Journal ArticleDOI
TL;DR: In this article, a weak solution for the Cauchy problem in unbounded domains has been shown for a class of fluid models with pressure-dependent viscosity in the context of implicit constitutive relations.
Abstract: In order to describe the behavior of various liquid-like materials at high pressures, incompressible fluid models with pressure dependent viscosity seem to be a suitable choice. In the context of implicit constitutive relations involving the Cauchy stress and the velocity gradient these models are consistent with standard procedures of continuum mechanics. Understanding the mathematical properties of the governing equations is connected with various types of idealizations, some of them lead to studies in unbounded domains. In this paper, we first bring up several characteristic features concerning fluids with pressure dependent viscosity. Then we study the three-dimensional flows of a class of fluids with the viscosity depending on the pressure and the shear rate. By means of higher differentiability methods we establish the large data existence of a weak solution for the Cauchy problem. This seems to be a first result that analyzes flows of considered fluids in unbounded domains. Even in the context of purely shear rate dependent fluids of a power-law type the result presented here improves some of the earlier works.

20 citations

Journal ArticleDOI
TL;DR: In this paper, two coupled, inhomogeneous relaxation equations for the friction pressure tensor and the alignment tensor were derived within the framework of irreversible thermodynamics for a specific geometry, viz. flow between flat plates, and for a velocity gradient of the form Γ0 + Γ1 cos Ωt with small Γ 1.
Abstract: Two coupled, inhomogeneous relaxation equations for the friction pressure tensor and the alignment tensor are derived within the framework of irreversible thermodynamics. These equations are solved for a specific geometry, viz. flow between flat plates, and for a velocity gradient of the form Γ0 + Γ1 cos Ωt with small Γ1. From the resulting relation between the (time-dependent) friction pressure tensor and the velocity gradient, the dynamic viscosity and the normal pressure can be inferred. The frequency dependence of the relevant viscosity coefficients is discussed. If Г0, the magnitude of the static part of the velocity gradient is large enough, a type of resonance behavior is found with the resonance frequency Ωres≈(1 + ξ)-1Γ0 where ξ is the ratio between the relation times of the friction pressure tensor and of the alignment tensor.

20 citations

Journal ArticleDOI
TL;DR: In this paper, a general decomposition of the stress tensor for incompressible fluids in terms of its components on a tensorial basis adapted to the local flow conditions is introduced.
Abstract: We introduce a general decomposition of the stress tensor for incompressible fluids in terms of its components on a tensorial basis adapted to the local flow conditions, which include extensional flows, simple shear flows, and any type of mixed flows. Such a basis is determined solely by the symmetric part of the velocity gradient and allows for a straightforward interpretation of the non-Newtonian response in any local flow conditions. In steady homogeneous flows, the material functions that represent the components of the stress on the adapted basis generalize and complete the classical set of viscometric functions used to characterize the response in simple shear flows. Such a general decomposition of the stress is effective in coherently organizing and interpreting rheological data from laboratory measurements and computational studies in non-viscometric steady flows of great importance for practical applications. The decomposition of the stress in terms with clearly distinct roles is also useful in developing constitutive models.

20 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202318
202233
2021127
2020116
2019134
201892