arXiv subjects

Wennan Zou

Publications and source records attributed to Wennan Zou.

14 recordsLinked to original sources

arXiv2026

Slip viscosity and strain-rate viscosity in Taylor-Couette laminar flows: Experimental falsification and end-wall effects

The viscous force should be shear force, the difference between the strain-rate viscosity and the slip viscosity is that the former has conjugate shear force, while the latter does not. The study in this paper verifies the physical authenticity of two viscosity models through Taylor Couette laminar flow experiments with inner and outer cylinders rotating at the same angular velocity, and numerically investigate the influence of relative cylinder spacing and rotational speed on the circumferential velocity under the slip model. The experimental results of LDV measurement with a relative cylinder spacing of 0.3 indicate that the maximum deviation from rigid-body rotation is about 0.86%, which is consistent with the theoretical prediction of slip viscosity model. The numerical simulations show that the end-walls have no effect under the strain-rate viscosity model; but when the slip viscosity model is introduced, the end-walls inevitably bring about the circumferential velocity profile changing along the axial direction, and result in a three-dimensional (3D) spiral streamline pattern influenced by the relative cylinder spacing and angular speed of cylinders.

physics.flu-dyn↗

arXiv2024

Slip topology of steady flows around a critical point: Taking the linear velocity field as an example

The flow of viscous fluids is considered as the aggregation of the motion of fluid particles when the fluid is conceived to be made up by an infinite number of particles. As an alternative of this conventional model, fluid motion could be understood as the slip of fluid layers with a molecular scale over each other, where the slip structures of fluid and their associated small-scale motion are characterized by an axial-vector-valued differential 1-form, called the vortex field. In this paper, in the case of steady flows we define the swirling degree of the velocity field at a point, and further the swirl field of the steady flow, to study the slip topology of fluid or the local streamline pattern around the critical point. The linear velocity field in the right real Schur form is used to carry out detailed analyses around the isolated critical point. Theoretical deduction and numerical test unveil the connection between the swirling degree and the swirl field, greatly make clear the topological property of slip structures of fluid in steady flows, especially in three-dimensional space.

physics.flu-dyn↗

arXiv2024

On the local streamline pattern of planar polynomial velocity field with nonzero linear part

The streamline pattern of planar polynomial velocity field is far from fully understood. In the community of fluid mechanics, most studies simply focus on the velocity gradient, or the linear part of the velocity field, but few studies on high-order terms. This paper is concerned with the local streamline pattern (LSP) of velocity field around an isotropic point. In virtue of the concept and method of dynamical systems, where the streamline pattern is equivalent to the phase portrait, we make clear the classification of LSPs of planar velocity fields with nonzero linear part, especially the cases where the determinant of velocity gradient vanishes at the isotropic point.

physics.flu-dyn↗

arXiv2023

Newton saw the truth -- on the nature of fluid flow and viscous interaction

The viscous interaction of fluid is understood as the response to deformation, which is proportional to the strain rate. This model has gradually become the standard since Stokes, and has become the basis of the classical flow theory, namely the Navier-Stokes (N-S) equations. However, it has never been accurately verified in the curved laminar flow. Here, a distinctive unambiguous simple experiment is designed to falsify the viscosity model of deformation, and instead a new model is proposed, that is, the viscous friction originates from the slip of fluid layering at molecular scale. Though Newton contributed the initial idea of slip viscosity, the new model cannot be formulated without the help of modern differential geometry. From the new model, the analytical solution of laminar Taylor-Couette (T-C) flow between two concentric cylinders can reproduce the result of the ideal experiment proposed by Newton as the outer cylinder being infinite, which was once considered a mistake of Newton. A significant difference with the solution of the N-S equations when the outer cylinder is relatively large can be used to distinguish the viscosity models, even for the simplest case with both cylinders rotating with the same angular velocity. The accurate measurement data by the LDA support the slip model, and the consequent flow theory inevitably leads to a new vision in turbulence research.

physics.flu-dyn↗

arXiv2022

Reconstructing fluid dynamics with micro-finite element

In the theory of the Navier-Stokes equations, the viscous fluid in incompressible flow is modelled as a homogeneous and dense assemblage of constituent "fluid particles" with viscous stress proportional to rate of strain. The crucial concept of fluid flow is the velocity of the particle that is accelerated by the pressure and viscous interaction around it. In this paper, by virtue of the alternative constituent "micro-finite element", we introduce a set of new intrinsic quantities, called the vortex fields, to characterise the relative orientation between elements and the feature of micro-eddies in the element, while the description of viscous interaction in fluid returns to the initial intuition that the interlayer friction is proportional to the slip strength. Such a framework enables us to reconstruct the dynamics theory of viscous fluid, in which the flowing fluid can be modelled as a finite covering of elements and consequently indicated by a space-time differential manifold that admits complex topological evolution.

physics.flu-dyn↗

arXiv2021

Thermoelectric and stress distributions around a smooth cavity in thermoelectric material

Thermoelectric materials have attracted more and more attention since they are friendly to the environment and have potentials for sustainable and renewable energy applications. As typically brittle semiconductors with low mechanical strength and always subjected to defects and damages, to clarify the stress concentration is very important in the design and implement of thermoelectric devices. The two-dimensional thermoelectric coupling problem due to a cavity embedded in an infinite isotropic homogeneous thermoelectric material, subjected to uniform electric current density or uniform energy flux, is studied, where the shape of the cavity is characterized by the Laurent polynomial, and the electric insulated and adiabatic boundary around the cavity are considered. The explicit analytic solutions of Kolosov-Muskhelishvili (K-M) potentials and rigid-body translation are carried out through a novel tactic. Comparing with the reported results, the new obtained are completely exact and possess a finite form. Some results of three typical cavities are presented to analyze the electric current densities (energy fluxes) and stresses around the tips. The main conclusions include: the distribution of thermoelectric field and stress at the tip obviously depends on the curvature of the contour and loading directions; for triangle and square with symmetrical tips, the maximum thermoelectric and stress concentration reach the maximum or minimum when the loading direction is parallel to or perpendicular to the symmetry axis of the tip, which is distinct to the extremum characteristics of pentagram with bimodal of curvature around the tip; the maximum thermoelectric and stress concentration appear near the maximum curvature point for most load directions, but not at the maximum curvature point.

physics.app-ph↗

arXiv2021

Thermal stress around a smooth cavity in a plate subjected to uniform heat flux

The two-dimensional thermoelastic problem of an adiabatic cavity in an infinite isotropic homogeneous medium subjected to uniform heat flux is studied, where the shape of the cavity is characterized by the Laurent polynomial. By virtue of a novel tactics, the obtained K-M potentials can be explicitly worked out to satisfy the boundary conditions precisely, and the possible translation of the cavity is also available. The new and explicit analytical solutions are compared with the those reported in literature and some serious problems are found and corrected. Finally, some discussions on the thermal stress concentration around the tips of three typical cavities are provided.

physics.app-ph↗

arXiv2020

No vortex in straight flows -- on the eigen-representations of velocity gradient

Velocity gradient is the basis of many vortex recognition methods, such as Q criterion, $Δ$ criterion, $λ_{2}$ criterion, $λ_{ci}$ criterion and $Ω$ criterion, etc.. Except the $λ_{ci}$ criterion, all these criterions recognize vortices by designing various invariants, based on the Helmholtz decomposition that decomposes velocity gradient into strain rate and spin. In recent years, the intuition of 'no vortex in straight flows' has promoted people to analyze the vortex state directly from the velocity gradient, in which vortex can be distinguished from the situation that the velocity gradient has couple complex eigenvalues. A specious viewpoint to adopt the simple shear as an independent flow mode was emphasized by many authors, among them, Kolar proposed the triple decomposition of motion by extracting a so-called effective pure shearing motion; Li et al. introduced the so-called quaternion decomposition of velocity gradient and proposed the concept of eigen rotation; Liu et al. further mined the characteristic information of velocity gradient and put forward an effective algorithm of Liutex, and then developed the vortex recognition method. However, there is another explanation for the increasingly clear representation of velocity gradient, that is the local streamline pattern based on critical-point theory. In this paper, the tensorial expressions of the right/left real Schur forms of velocity gradient are clarified from the characteristic problem of velocity gradient. The relations between the involved parameters are derived and numerically verified. Comparing with the geometrical features of local streamline pattern, we confirm that the parameters in the right eigen-representation based on the right real Schur form of velocity gradient have good meanings to reveal the local streamline pattern. Some illustrative examples from the DNS data are presented.

physics.flu-dyn↗

arXiv2019

Geometrical and topological description of chirality-relevant flow structures

Issues relevant to the flow chirality and structure are focused, while the new theoretical results, including even a distinctive theory, are introduced. However, it is hope that the presentation, with a low starting point but a steep rise, is appropriate for a broader spectrum of audiences ranging from students to researchers, thus illustrations of differential forms and relevant basic topological concepts are also offered, followed by the demonstration with formulation of differential forms of the classical Navier-Stokes flow theory and the discussions of recent studies in fundamental fluid mechanics and turbulence.

physics.flu-dyn↗

arXiv2018

Two Irreducible Functional Bases of Isotropic Invariants of A Fourth Order Three-Dimensional Symmetric and Traceless Tensor

The elasticity tensor is one of the most important fourth order tensors in mechanics. Fourth order three-dimensional symmetric and traceless tensors play a crucial role in the study of the elasticity tensors. In this paper, we present two isotropic irreducible functional bases of a fourth order three-dimensional symmetric and traceless tensor. One of them is the minimal integrity basis introduced by Smith and Bao in 1997. It has nine homogeneous polynomial invariants of degrees two, three, four, five, six, seven, eight, nine and ten, respectively. We prove that it is also an irreducible functional basis. The second irreducible functional basis also has nine homogeneous polynomial invariants. It has no quartic invariant but has two sextic invariants. The other seven invariants are the same as those of the Smith-Bao basis. Hence, the second irreducible functional basis is not contained in any minimal integrity basis.

math-ph↗

arXiv2018

Irreducible Function Bases of Isotropic Invariants of A Third Order Three-Dimensional Symmetric and Traceless Tensor

Third order three-dimensional symmetric and traceless tensors play an important role in physics and tensor representation theory. A minimal integrity basis of a third order three-dimensional symmetric and traceless tensor has four invariants with degrees two, four, six and ten respectively. In this paper, we show that any minimal integrity basis of a third order three-dimensional symmetric and traceless tensor is also an irreducible function basis of that tensor, and there is no polynomial syzygy relation among the four invariants of that basis, i.e., these four invariants are algebraically independent.

math-ph↗

arXiv2018

An Irreducible Function Basis of Isotropic Invariants of A Third Order Three-Dimensional Symmetric Tensor

In this paper, we present an eleven invariant isotropic irreducible function basis of a third order three-dimensional symmetric tensor. This irreducible function basis is a proper subset of the Olive-Auffray minimal isotropic integrity basis of that tensor. The octic invariant and a sextic invariant in the Olive-Auffray integrity basis are dropped out. This result is of significance to the further research of irreducible function bases of higher order tensors.

math-ph↗

arXiv2018

Isotropic Polynomial Invariants of the Hall Tensor

The Hall tensor emerges from the study of the Hall effect, an important magnetic effect observed in electric conductors and semiconductors. The Hall tensor is third order and three dimensional, whose first two indices are skew-symmetric. In this paper, we investigate the isotropic polynomial invariants of the Hall tensor by connecting it with a second order tensor via the third order Levi-Civita tensor. We propose a minimal isotropic integrity basis with 10 invariants for the Hall tensor. Furthermore, we prove that this minimal integrity basis is also an irreducible isotropic function basis of the Hall tensor.

math-ph↗

arXiv2011

A Rational Model of Large-Scale Motion in Turbulence

A rational theory is proposed to describe the large-scale motion in turbulence. The fluid element with inner orientational structures is proposed to be the building block of fluid dynamics. The variance of the orientational structures then constitutes new fields suitable to describe the vortex state in turbulence. When the fluid element is assumed to be an open subsystem, the differentiable manifold description of turbulence ought to be set up, and the complete fluid dynamics can be deduced from a variational calculus on the constructed Lagrangian dissipation energy density. The derived dynamical equations indicate that the vortex evolution is naturally related with the angular momentum balance.

physics.flu-dyn↗