Velocity gradient

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

Theory of linear viscoelasticity of cholesteric liquid crystals

Abstract: The theory of linear viscoelasticity of rod-like cholesteric liquid crystals subjected to small-amplitude oscillatory shear flow is formulated and applied to the cholesteric helix along the flow, velocity gradient, and vorticity directions. Expressions for the zero- and infinite-frequency viscosities are derived and their ordering is predicted. Based on the classical ordering of the Miesowicz shear viscosities and anisotropies of torque coefficients, it is found that the largest (smallest) zero-frequency viscosity obtains with the helix along the flow (gradient) direction. In addition, the difference between the zero- and infinite-frequency viscosities is found to be sensitive to the helix orientation, such that it is largest (smallest) when the helix is along the flow (gradient) direction. The complex viscosity corresponds to a viscoelastic material with a single relaxation time. The relaxation time depends on the Frank elastic constants involved in the deformation, such that when the helix is along the vorticity it is twist dependent, and splay–bend otherwise. The strength of the viscoelasticity is largest (smallest) when the helix is along the flow (gradient) direction. The hard-rod theory of Doi is used to confirm the predicted dependence of the strength of the viscoelastic response on the cholesteric helix orientation.

Shear of Diblock Copolymer Lamellae: Width Changes and Undulational Instabilities

Abstract: We investigate the effect of oscillatory shear on the lamellar spacing in melts of symmetric diblock copolymers in the strong segregation limit. We find that the equilibrium lamellar spacing decreases. The modulus due to entanglements plays an important role. We further argue that before equilibrium is reached the layers will show an undulational instability in the direction perpendicular to the velocity and the velocity gradient

A hybrid RANS/LES simulation of high-Reynolds-number channel flow using additional filtering at the interface

Abstract: A hybrid method combining large eddy simulation (LES) with the Reynolds-averaged Navier-Stokes (RANS) equation is used to simulate a turbulent channel flow at high Reynolds number. It is known that the mean velocity profile has a mismatch between the RANS and LES regions in hybrid simulations of a channel flow. The velocity mismatch is reproduced and its dependence on the location of the RANS/LES interface and on the type of RANS model is examined in order to better understand its properties. To remove the mismatch and to obtain better velocity profiles, additional filtering is applied to the velocity components in the wall-parallel planes near the interface. The additional filtering was previously introduced to simulate a channel flow at low Reynolds number. It is shown that the filtering is effective in reducing the mismatch even at high Reynolds number. Profiles of the velocity fluctuations of runs with and without the additional filtering are examined to help understand the reason for the mismatch. Due to the additional filtering, the wall-normal velocity fluctuation increases at the bottom of the LES region. The resulting velocity field creates the grid-scale shear stress more efficiently, and an overestimate of the velocity gradient is removed. The dependence of the velocity profile on the grid point number is also investigated. It is found that the velocity gradient in the core region is underestimated in the case of a coarse grid. Attention should be paid not only to the velocity mismatch near the interface but also to the velocity profile in the core region in hybrid simulations of a channel flow at high Reynolds number.

A constraint for the subgrid-scale stresses in the logarithmic region of high Reynolds number turbulent boundary layers: A solution to the log-layer mismatch problem

Abstract: This paper addresses one of the most persisting problems in wall-modeled large eddy simulation (LES): the overshoot of the mean velocity gradient near the wall, often referred to as the “log-layer mismatch” problem. An analysis of the relationship between turbulent kinetic energy budgets and mean velocity gradient is elaborated for both direct numerical simulations and LES of fully developed channel flow at high Reynolds number. Based on the analysis, a self-adaptive Smagorinsky model for LES of high-Reynolds-number boundary layer flows is proposed, in which the Smagorinsky coefficient is dynamically adjusted so that a logarithmic mean velocity distribution is captured. The model is then implemented in a second-order finite-volume code, and applied to a high-Reynolds-number channel flow with rough walls. We find that the desired logarithmic mean velocity distribution is well predicted for different resolutions and grid aspect ratios.

X-ray attenuation measurements in a cavitating mixing layer for instantaneous two-dimensional void ratio determination

Abstract: The purpose of this experimental study was to analyze a two-dimensional cavitating shear layer. The global aim of this work was to obtain a better understanding and modeling of cavitation phenomenon in a 2D turbulent sheared flow which can be considered as quite representative of cavitating rocket engine turbopomp inducers. This 2D mixing layer flow provided us a well documented test case which can be used for the characterization of the cavitation effects in sheared flows. The development of a velocity gradient was observed inside a liquid water flow: Kelvin-Helmholtz instabilities developed at the interface. Vaporizations and implosions of cavitating structures inside the vortices were observed. X-ray attenuation measurements were performed to estimate the amount of vapor present inside the mixing area. Instantaneous two-dimensional void ratio fields were acquired. The real spatial resolutions are 0.5 mm with 2000 fps and 1.5 mm with 20 000 fps. The effective time resolution is equal to the camera frame rate up to a 19% void ratio variation between two consecutive images. This seems to be sufficient in the context of the present flow configuration. The two-phase structures present inside the mixing area were analyzed at three different cavitation levels and their behaviors were compared to non-cavitating flow dynamic. Convection velocities and vortices shedding frequencies were estimated. Results show that vapor was transported by the turbulent velocity field. Statistical analysis of the void ratio signal was carried out up to the fourth order moment. This study provided a global understanding of the cavitating structure evolution and of the cavitation effects on turbulent sheared flows.