scholarly journals Особенности релаксации тензора напряжения в микроскопическом объеме нематической фазы под действием сильного электрического поля

2018 ◽  
Vol 60 (2) ◽  
pp. 405
Author(s):  
А.В. Захаров

AbstractA numerical study of new regimes of reorientation of director field n̂ , velocity v , and components of stress tensor σ_ ij ( ij = x , y , z ) of nematic liquid crystal (LC) encapsulated in a rectangular channel under the action of a strong electric field E directed at angle $$\alpha \left( {\sim\frac{\pi } {2}} \right)$$ α ( ∼ π 2 ) to the horizontal surfaces bounding the LC channel is proposed. The numerical calculations performed in the framework of nonlinear generalization of the classical Eriksen-Leslie theory have shown that at certain relations between the torques and momenta affecting the unit LC volume and E ≫ E _th, transition periodic structures can emerge during reorientation of n̂ , if the corresponding distortion mode has the fastest response, and, thus, suppress all other modes. Rotating domains originating within this process decrease the energy dissipation rate and create more favorable regimes of the director field reorientation, as compared with the uniform rotational displacement.

2019 ◽  
Vol 9 (3) ◽  
pp. 436 ◽  
Author(s):  
Shenglong Gu ◽  
Fuping Bo ◽  
Min Luo ◽  
Ehsan Kazemi ◽  
Yunyun Zhang ◽  
...  

This paper presents a numerical study of the hydraulic jump on corrugated riverbed using the Smoothed Particle Hydrodynamics (SPH) method. By simulating an experimental benchmark example, the SPH model is demonstrated to predict the wave profile, velocity field, and energy dissipation rate of hydraulic jump with good accuracy. Using the validated SPH model, the dynamic evolvement of the hydraulic jump on corrugated riverbed is studied focusing on the vortex pattern, jump length, water depth after hydraulic jump, and energy dissipation rate. In addition, the influences of corrugation height and length on the characteristics of hydraulic jump are parametrically investigated.


Water ◽  
2021 ◽  
Vol 13 (15) ◽  
pp. 2005
Author(s):  
Milad Mohammadi ◽  
Mohammad Nazari-Sharabian ◽  
Moses Karakouzian

We present a new method to evaluate the hydraulic jump characteristics in a horizontal rectangular channel with a positive step. We considered the flow curvature effect and the free surface’s small rise at the A-type hydraulic jump’s end. First, we present a novel method to give jump length estimation based on the similarity of the jump and the turbulent wall-jet, considering the pressure gradient. Then, considering the jump as a curvilinear flow and using a one-dimensional momentum equation, we present an accurate expression for the conjugate flow depth regarding the initial Froude number and step height. Finally, we compute the jump’s energy dissipation rate. Compared to the theoretical models for conjugate flow depth in a hydraulic jump, the proposed equation in this study fit the experimental data better, even for high steps and large initial Froude numbers. However, for low Froude numbers (F1 < 5), the equation was less accurate in estimating the jump length. Regarding the jump’s energy dissipation rate, the results agreed well with the experimental data from previous investigations. However, it is noted that the increased energy dissipation rate dwindled in larger Froude numbers.


Author(s):  
Michael Maurer ◽  
Jens von Wolfersdorf ◽  
Michael Gritsch

An experimental and numerical study was conducted to determine the thermal performance of V-shaped ribs in a rectangular channel with an aspect ratio of 2:1. Local heat transfer coefficients were measured using the steady state thermochromic liquid crystal technique. Periodic pressure losses were obtained with pressure taps along the smooth channel sidewall. Reynolds numbers from 95,000 to 500,000 were investigated with V-shaped ribs located on one side or on both sides of the test channel. The rib height-to-hydraulic diameter ratios (e/Dh) were 0.0625 and 0.02, and the rib pitch-to-height ratio (P/e) was 10. In addition, all test cases were investigated numerically. The commercial software FLUENT™ was used with a two-layer k-ε turbulence model. Numerically and experimentally obtained data were compared. It was determined that the heat transfer enhancement based on the heat transfer of a smooth wall levels off for Reynolds numbers over 200,000. The introduction of a second ribbed sidewall slightly increased the heat transfer enhancement whereas the pressure penalty was approximately doubled. Diminishing the rib height at high Reynolds numbers had the disadvantage of a slightly decreased heat transfer enhancement, but benefits in a significantly reduced pressure loss. At high Reynolds numbers small-scale ribs in a one-sided ribbed channel were shown to have the best thermal performance.


1994 ◽  
Vol 5 (4) ◽  
pp. 537-557 ◽  
Author(s):  
M. Bertsch ◽  
R. Dal Passo ◽  
R. Kersner

We study the semi-empirical b—ε model which describes the time evolution of turbulent spots in the case of equal diffusivity of the turbulent energy density b and the energy dissipation rate ε. We prove that the system of two partial differential equations possesses a solution, and that after some time this solution exhibits self-similar behaviour, provided that the system has self-similar solutions. The existence of such self-similar solutions depends upon the value of a parameter of the model.


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