Direct numerical simulation study of the interaction between the polymer effect and velocity gradient tensor in decaying homogeneous isotropic turbulence

Direct numerical simulation of decaying homogeneous isotropic turbulence （DHIT） of a polymer solution is performed. In order to understand the polymer effect on turbulence or additive-turbulence interaction, we directly investigate the influence of polymers on velocity gradient tensor including vorticity and strain. By visualizing vortex tubes and sheets, we observe a remarkable inhibition of vortex structures in an intermediate-scale field and a small-scale field but not for a large scale field in DHIT with polymers. The geometric study indicates a strong relevance among the vorticity vector, rate-of-strain tensor, and polymer conformation tensor. Joint probability density functions show that the polymer effect can increase ＂strain generation resistance＂ and ＂vorticity generation resistance＂, i.e., inhibit the generation of vortex sheets and tubes, ultimately leading to turbulence inhibition effects.

Uniform decomposition of velocity gradient tensor

In this paper,the principal decomposition of the velocity gradient tensor[∇v]is discussed in 3 cases based on the discriminant∆:∆<0 with 1 real eigen value and a pair of conjugate complex eigen values,∆>0 with 3 distinct real eigen values,and∆=0 with 1 or 2 distinct real eigen values.The velocity gradient tensor can also be classified as rotation point,which can be decomposed into three parts,i.e.,rotation[R],shear[S]and stretching/compression[SC],and non-rotation point,we defined a new resistance term[L],and the tensor can be decomposed into three parts,i.e.,resistance[L],shear[S]and stretching/compression[SC].Example matric are also displayed to demonstrate the new decomposition.Connections of principal decomposition between 3 different cases,and between Resistance and Liutex will also be discussed.

Optimization of multi-stage velocity gradients in a cylindrical fluidized bed flocculator

Flocculation time is conventionally believed to be proportional to the fiocculation effciency of a cylindrical fluidized bed flocculator. However, in a single-stage velocity gradient situation, the flocculation efficiency decreases when the optimal flocculation time is exceeded. A multi-stage velocity gradient was established in a cylindrical fluidized bed flocculator, based on the hydraulic classification theory. This multi-stage velocity gradient fluidized bed flocculator （MGF） created a more suitable environment for floc growth and protection, which was confirmed by the size distribution of flocs along the bed height. Correspondingly, the abatement efficiencies for Kaolin slurry and dyed wastewater treatment in the MGF were enhanced by 5-10%, and by 7-20%, respectively, compared with those in the single-stage velocity gradient fluidized bed flocculators （SGFs）. The initial bed height distribution ratio along the velocity gradients was an important factor for MGF optimization.

Studying turbulence structure near the wall in hydrodynamic flows:An approach based on the Schur decomposition of the velocity gradient tensor

The Schur decomposition of the velocity gradient tensor(VGT)is an alternative to the classical Cauchy-Stokes decomposition into rotation rate and strain rate components.Recently,there have been several strands of work that have employed this decomposition to examine the physics of turbulence dynamics,including approaches that combine the Schur and Cauchy-Stokes formalisms.These are briefly reviewed before the latter approach is set out.This partitions the rotation rate and strain rate tensors into normal/local and non-normal/non-local contributions.We then study the relation between the VGT dynamics and ejection-sweep events in a channel flow boundary-layer.We show that the sweeps in particular exhibit novel behaviour compared with either the other quadrants,or the flow in general,with a much-reduced contribution to the dynamics from the non-normal terms above the viscous sub-layer.In particular,the reduction in the production term that is the interaction between the non-normality and the normal straining reduces in the log-layer as a consequence of an absence of alignment between the non-normal vorticity and the strain rate eigenvectors.There have been early forays into using the Schur transform approach for subgrid-scale modelling in large-eddy simulation(LES)and this would appear to be an exciting way forward.

Dynamics and geometry of developing planar jets based on the invariants of the velocity gradient tensor

Based on the direct numerical simulation （DNS）, the developing planar jets under different initial conditions, e.g., the con- ditions of the exit Reynolds number and the exit mean velocity profile, are investigated. We mainly focus on the characteristics of the invariants of the velocity gradient tensor, which provides insights into the evolution of the dynamics and the geometry of the planar jets along with the flow transition. The results show that the initial flow near the jet exit is strongly predominated by the dissipation over the enstrophy, the flow transition is accompanied by a severe rotation and straining of the flow elements, where the vortex structure evolves faster than the fluid element deformation, in the fully-developed state, the irrotational dissipation is dominant and the most probable geometry of the fluid elements should remain between the biaxial stretching and the axisymmetric stretching. In addition, with a small exit Re and a parabolic profile for the exit mean streamwise velocity, the decay of the mean flow field and the magnitude of the turbulent variables will be strengthened in the process of the flow transition, however, a large exit Re will promote the flow transition to the fully-developed state. The cross-impact between the exit Re and the exit mean velocity profile is also observed in the present study.

Velocity gradient elasticity for nonlinear vibration of carbon nanotube resonators

In this study,for the first time,we investigate the nonlocality superimposed to the size effects on the nonlinear dynamics of an electrically actuated single-walled carbon-nanotube-based resonator.We undertake two models to capture the nanostructure nonlocal size effects:the strain and the velocity gradient theories.We use a reduced-order model based on the differential quadrature method(DQM)to discretize the goverming nonlinear equation of motion and acquire a discretized-parameter nonlinear model of the system.The structural nonlinear behavior of the system assuming both strain and velocity gradient theories is investigated using the discretized model.The results suggest that nonlocal and size effects should not be neglected because they improve the prediction of corresponding dynamic amplitudes and,most importantly,the critical resonant frequencies of such nanoresonators.Neglcting these effects may impose a considerable source of error,which can be amended using more accurate modeling techniques.

Effects of Transverse Temperature Gradient on the Rotor Velocity in an Ultrasonic Motor

As a result of the nonlinear effect, acoustic streaming has been widely used for increasing the transport coefficient or driving a rotor, for example, in resonant cavities and non-contact ultrasonic motors. It has been demonstrated by experiments that a temperature gradient transverse to the wave propagating direction can significantly increase the velocity of the streaming flows in resonant cavities. To check whether the transverse temperature gradient can also increase the working velocity of acoustic streaming-driven motors, we investigate this issue by numerically solving the hydrodynamic equations. It is found that the velocity of the rotor only weakly depends on the transverse temperature gradient, e.g., even with a temperature difference of 40℃ between the rotor and the stator, the velocity increases only -8.8%.

Prediction of boundary shear stress distribution in straight open channels using velocity distribution

Conventional methods for measuring local shear stress on the wetted perimeter of open channels are related to the measurement of the very low velocity close to the boundary.Measuring near-zero velocity values with high fluctuations has always been a difficult task for fluid flow near solid boundaries.To solve the observation problems,a new model was developed to estimate the distribution of boundary shear stress from the velocity distribution in open channels with different cross-sectional shapes.To estimate the shear stress at a point on the wetted perimeter by the model,the velocity must be measured at a point with a known normal distance to the boundary.The experimental work of some other researchers on channels with various cross-sectional shapes,including rectangular,trapezoidal,partially full circular,and compound shapes,was used to evaluate the performance of the proposed model.Optimized exponent coefficients for the model were found using the multivariate Newton method with the minimum of the mean absolute percentage error(MAPE)between the model and experimental data as the objective function.Subsequently,the calculated shear stress distributions along the wetted perimeter were compared with the experimental data.The most important advantage of the proposed model is its inherent simplicity.The mean MAPE value for the seven selected cross-sections was 6.9%.The best results were found in the cross-sections with less discontinuity of the wetted perimeter,including the compound,trapezoidal,and partially full circular pipes.In contrast,for the rectangular cross-section with an angle between the bed and walls of 90°,MAPE increased due to the large discontinuities.

Mathematical foundation of Liutex theory

Liutex is a mathematical definition of vortex,which is called the third generation of vortex definition and identification.This paper introduces the mathematical foundation of the Liutex theoretical system including differences in definition and operations between tensor/vector and matrix.The right version of velocity gradient tensor matrix is given to correct the old version which has been widely distributed by many mathematics and fluid dynamics textbooks.A unique velocity gradient principal matrix is provided.The mathematical foundation for Liutex definition is given.The coordinate rotation(Q-and P-rotation)for principal coordinate system and principal matrix is derived,which is the key issue of the new fluid kinematics.The divergence of velocity gradient tensor is given in different forms which may be beneficial in developing new governing equations for fluid dynamics.

Stretching and shearing contamination analysis for Liutex and other vortex identification methods

The newly developed vortex-identification method,Liutex,has provided a new systematic description of the local fluid rotation,which includes scalar,vector,and tensor forms.However,the advantages of Liutex over the other widely used vortexidentification methods such as Q,Δ,λ2,andλci have not been realized.These traditional methods count on shearing and stretching as a part of vortex strength.But,in the real flow,shearing and stretching do not contribute to fluid rotation.In this paper,the decomposition of the velocity gradient tensor is conducted in the Principal Coordinate for uniqueness.Then the contamination effects of stretching and shearing of the traditional methods are investigated and compared with the Liutex method in terms of mathematical analysis and numerical calculations.The results show that the Liutex method is the only method that is not affected by either stretching or shear,as it represents only the local fluid rigid rotation.These results provide supporting evidence that Liutex is the superior method over others.

Microstructure-dependent Band Gaps for Elastic Wave Propagation in a Periodic Microbeam Structure

A new model for producing band gaps for flexural elastic wave propagation in a periodic microbeam structure is developed using an extended transfer matrix method and a non-classical Bernoulli–Euler beam model that incorporates the strain gradient,couple stress and velocity gradient effects.The band gaps predicted by the new model depend on the three microstructure-dependent material parameters of each constituent material,the beam thickness,the unit cell length and the volume fraction.A parametric study is conducted to quantitatively illustrate these factors.The numerical results reveal that the first band gap frequency range increases with the increases of the three microstructure-dependent material parameters,respectively.In addition,the band gap size predicted by the current model is always larger than that predicted by the classical model,and the difference is large for very thin beams.Furthermore,both the unit cell length and volume fraction have significant effects on the band gap.

The experiment and analysis of transitional flow in pipe

The transitional flow in a pipe is important for delivery, but its characteristics remain to be explored. In this paper, the two-dimensional laser Doppler velocimetry （LDV） is used for the study, focusing on the attenuation characteristics of the axial velocity, the variation of the velocity gradient, the effect of the angle between the axis and the resultant velocity vector, and the relationship between the energy coefficient and the flow state. The attenuation characteristics of the axial velocity along the radial direction are obtained. It is shown that with the increase of the Reynolds number, the change rate of the velocity gradient slows down with a similar distribution, and a rapid decrease is seen in the near wall region. The amplitude and the frequency of the angular variation are obviously improved with the increase of the Reynolds number. The instability of the velocity field is enhanced with the increase of the energy coefficient.