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Hua-Shu Dou

Publications and source records attributed to Hua-Shu Dou.

At least 19 recordsLinked to original sources
arXiv2026

Effect of gap width on turbulent transition in Taylor-Couette flow

Simulations of the transitional flow in Taylor-Couette configuration are carried out to study the effect of the gap width on turbulent transition. The research results show that, under the same radius and the rotating speed of the inner cylinder, as the gap width increases, the flow becomes more stable. It is discovered that the average velocity distribution in the gap approaches the free vortex flow as the width increase and the stability of the flow is enhanced. It is found that, as the gap width increases, the maximum of the energy gradient function (from the energy gradient theory) in the gap decreases, which delays the turbulent transition. As such, the larger the gap width, the later the transition occurs. As the gap width increases, the Reynolds number based on the gap width alone is not able to characterize the flow behavior in Taylor-Couette flows, and the effect of the radius ratio should be taken into account.

physics.flu-dyn↗
arXiv2026

Inverse Energy Cascade in Turbulent Taylor-Couette Flows

The inverse energy cascade in turbulent Taylor-Couette flow is studied in line with the results of the large eddy simulation. The simulation results show that the inverse energy cascade first occurs within the core region of the flow channel of the Taylor-Couette flow at higher Reynolds number. It is uncovered that this phenomenon is induced by the pulsed zero shear stress resulting from the singularities of the Navier-Stokes equation. In the core area between the two cylinders, the shear stress is nearly zero at higher Reynolds number. The turbulence generated there has high turbulent energy due to discontinuity of the tangential velocity. Since the energy transfer between the fluid layers is inhibited due to the low shear stress, the turbulent energy cannot be transferred along the radial direction, and small-scale vortices with high turbulent energy are produced. These small-scale vortices are located with the large-scale vortices and cannot be dissipated owing to low shear stress. A peak in the energy spectrum at middle frequency (or wave number) is formed due to the concentration of the small-scale vortices. As the number of the singular points of the Navier-Stokes equation increases with the increasing Reynolds number, the region with zero shear stress expands along the radial direction, intensifying nonlinear instability and energy accumulation. This, in turn, leads to more prominent peaks in the energy spectrum, resulting in a more pronounced inverse energy cascade.

physics.flu-dyn↗
arXiv2026

Solitary wave structure of transitional flow in the wake of a sphere

The soliton-like coherent structure (SCS), which has been verified to exist in both transitional and turbulent boundary layers1-4, still poses a challenge in the understanding of its formation and behavior. In our previous study (Niu et al.5), the SCS was also found to exist in the transitional wake flow behind a sphere. In present study, the formation and evolution of the SCS is further investigated at four Reynolds numbers by numerical simulation. The results show that at the early stage of the turbulence transition, the SCS appears as a form of wave packet during the Tollmien-Schlichting (T-S) wave stage. With the increase of the Reynolds number, the SCS reaches its maximum amplitude downstream where the velocity discontinuity occurs. This position is located after the breakdown of the T-S wave and the three-dimensional structure is formed. Then, the SCS conserves its shape and amplitude over a long distance downstream. The relationships among the SCS, the spikes, the vortex structures, and the high-shear layers are further analyzed. It is found that the SCS in the wake flow has similarities to the phenomena observed in boundary layer flows during the turbulent transition. The vortex structures and high-shear layers mostly wrap around the border of the SCS. The vortex structure is considered to be as a consequence of the development of the SCS rather than its cause.

physics.flu-dyn↗
arXiv2022

No Existence and Smoothness of Solution of the Navier-Stokes Equation

The Navier-Stokes equation can be written in a form of Poisson equation. For laminar flow in a channel (plane Poiseuille flow), the Navier-Stokes equation has a non-zero source term and a non-zero solution within the domain. For transitional flow, the velocity profile is distorted, and an inflection point or kink appears on the velocity profile, at a sufficiently high Reynolds number and large disturbance. In the vicinity of the inflection point or kink on the distorted velocity profile, we can always find a point where the source term is zero. At this point, the Poisson equation is singular, due to the zero source term, and has no solution at this point due to singularity. It is concluded that there exists no smooth and physically reasonable solutions of the Navier-Stokes equation for transitional flow and turbulence in the global domain due to singularity.

physics.flu-dyn↗
arXiv2020

A universal equation for calculating the energy gradient function in shear driven flows using the energy gradient theory

The energy gradient theory was proposed in our previous studies. The mechanism of flow instability is very different in shear driven flows from pressure driven flows. In present paper, the relationship for the energy variation, work done, and energy dissipation in unit volumetric fluid of incompressible flow is derived. A universal equation for calculating the energy gradient function in shear driven flows is presented. With the calculation of the energy gradient function which is a field variable and is considered as a local Reynolds number, the stability of a basic flow can be analyzed. The method can be applied to parallel flows, curved flows, and various complex flows.

physics.flu-dyn↗
arXiv2020

Singularity of Navier-Stokes Equations Leading to Turbulence

Singularity of Navier-Stokes equations is uncovered for the first time which explains the mechanism of transition of a smooth laminar flow to turbulence. It is found that when an inflection point is formed on the velocity profile in pressure driven flows, velocity discontinuity occurs at this point. Meanwhile, pressure pulse is produced at the discontinuity due to conservation of the total mechanical energy. This discontinuity makes the Navier-Stokes equations be singular and causes the flow to become indefinite. The analytical results show that the singularity of the Navier-Stokes equations is the cause of turbulent transition and the inherent mechanism of sustenance of fully developed turbulence. Since the velocity is not differentiable at the singularity, there exist no smooth and physically reasonable solutions of Navier-Stokes equations at high Reynolds number (beyond laminar flow). The negative spike of velocity and the pulse of pressure due to discontinuity have obtained agreement with experiments and simulations in literature qualitatively.

physics.flu-dyn↗
arXiv2019

Influence of Magnetic Force on the Flow Stability in a Rectangular duct

The stability of the flow under the magnetic force is one of the classical problems in fluid mechanics. In this paper, the flow in a rectangular duct with different Hartmann (Ha) number is simulated. The finite volume method and the SIMPLE algorithm are used to solve a system of equations and the energy gradient theory is then used to study the (associated) stability of magnetohydrodynamics (MHD). The flow stability of MHD flow for different Hartmann (Ha) number, from Ha=1 to 40, at the fixed Reynolds number, Re=190 are investigated. The simulation is validated firstly against the simulation in literature. The results show that, with the increasing Ha number, the centerline velocity of the rectangular duct with MHD flow decreases and the absolute value of the gradient of total mechanical energy along the streamwise direction increases. The maximum of K appears near the wall in both coordinate axis of the duct. According to the energy gradient theory, this position of the maximum of K would initiate flow instability (if any) than the other positions. The higher the Hartmann number is, the smaller the K value becomes, which means that the fluid becomes more stable in the presence of higher magnetic force. As the Hartmann number increases, the K value in the parallel layer decreases more significantly than in the Hartmann layer. The most dangerous position of instability tends to migrate towards wall of the duct as the Hartmann number increases. Thus, with the energy gradient theory, the stability or instability in the rectangular duct can be controlled by modulating the magnetic force.

physics.flu-dyn↗
arXiv2019

Simulation and Instability Investigation of the Flow around a Cylinder between Two Parallel Walls

The two-dimensional flows around a cylinder between two parallel walls at Re=40 and Re=100 are simulated with computational fluid dynamics (CFD). The governing equations are Navier-Stokes equations. They are discretized with finite volume method (FVM) and the solution is iterated with PISO Algorithm. Then, the calculating results are compared with the numerical results in literature, and good agreements are obtained. After that, the mechanism of the formation of Karman vortex street is investigated and the instability of the entire flow field is analyzed with the energy gradient theory. It is found that the two eddies attached at the rear of the cylinder have no effect on the flow instability for steady flow, i.e., they don't contribute to the formation of Karman vortex street. The formation of Karman vortex street originates from the combinations of the interaction of two shear layers at two lateral sides of the cylinder and the absolute instability in the cylinder wake. For the flow with Karman vortex street, the initial instability occurs at the region inner a vortex downstream of the wake and the center of a vortex firstly loses its stability inner a vortex. For pressure driven flow, it is confirmed that the inflection point on the time-averaged velocity profile leads to the instability. It is concluded that the energy gradient theory is potentially applicable to study the flow stability and to reveal the mechanism of turbulent transition.

physics.flu-dyn↗
arXiv2019

Effect of Rotational Speed on the Stability of Two Rotating Side-by-side Circular Cylinders at Low Reynolds Number

Flow around two rotating side-by-side circular cylinders of equal diameter D is numerically studied at the Reynolds number Re=40-200 and various rotation rate theta_i. The incoming flow is assumed to be two-dimensional laminar flow. The governing equations are the incompressible Navier-Stokes equations and solved by the finite volume method (FVM). The ratio of the center-to-center spacing to the cylinder diameter is T/D=2. The objective of the present work is to investigate the effect of rotational speed and Reynolds number on the stability of the flow. The simulation results are compared with the experimental data and a good agreement is achieved. The stability of the flow is analyzed by using the energy gradient theory, which produces the energy gradient function K to identify the region where the flow is the most prone to be destabilized and the degree of the destabilization. Numerical results reveal that K is the most significant at the separated shear layers of the cylinder pair. With Re increases, the length of the wake is shorter and the vortex shedding generally exhibits a symmetrical distribution for theta_i <theta_crit. It is also shown that the unsteady vortex shedding can be suppressed by rotating the cylinders in the counter-rotating mode.

physics.flu-dyn↗
arXiv2018

Numerical simulation of flow instability and heat transfer of natural convection in a differentially heated cavity

This paper numerically investigates the physical mechanism of flow instability and heat transfer of natural convection in a cavity with thin fin(s). The left and the right walls of the cavity are differentially heated. The cavity is given an initial temperature, and the thin fin(s) is fixed on the hot wall in order to control the heat transfer. The finite volume method and the SIMPLE algorithm are used to simulate the flow. Distributions of the temperature, the pressure, the velocity and the total pressure are obtained. Then, the energy gradient theory is employed to study the physical mechanism of flow instability and the effect of the thin fin(s) on heat transfer. Based on the energy gradient theory, the energy gradient function K represents the characteristic of flow instability. It is observed from the simulation results that the positions where instabilities take place in the temperature contours accord well with those of higher K value, which demonstrates that the energy gradient theory reveals the physical mechanism of flow instability. Furthermore, the effects of the fin length, the fin position, the fin number, and Ra on heat transfer are investigated. It is found that the effect of the fin length on heat transfer is negligible when Ra is relatively high. When there is only one fin, the most efficient heat transfer rate is achieved as the fin is fixed at the middle height of the cavity. The fin blocks heat transfer with a relatively small Ra, but the fin enhances heat transfer with a relatively large Ra. The fin(s) enhances heat transfer gradually with the increase of Ra under the influence of the thin fin(s). Finally, a linear correlation of Kmax with Ra is obtained which reveals the physical mechanism of natural convection from different approaches.

physics.flu-dyn↗
arXiv2018

Analysis of vortex breakdown in an enclosed cylinder based on the energy gradient theory

Numerical simulation is carried out to study the phenomenon of vortex breakdown in an enclosed cylinder. The energy gradient theory is used to explain the vortex breakdown in the cylinder with consideration of centrifugal force, Coriolis force, angular momentum and azimuthal vorticity. The research results show that the large value of energy gradient function K is mainly located at the centerline and the region between the circulation vortices on both sides of the cylinder and the vortex breakdown bubbles at the centerline. It is found that the position of the local peak value of the energy gradient function K at the centerline corresponds to the location of vortex breakdown first occurrence. The position of the local peak value of K function in horizontal direction corresponds to the velocity inflection points except for the centerline. The vortex breakdown is mainly determined by the high K value at the centerline for low aspect ratio. The influence of the region of high K value between the circulation vortices on both sides of the cylinder and the vortex breakdown bubbles at the centerline becomes larger with the increase of the aspect ratio. The occurrence and development of the vortex breakdown bubble may be affected by the region of high K value between the circulation vortices on both sides of the cylinder and the vortex breakdown bubbles at the centerline for high aspect ratio.

physics.flu-dyn↗
arXiv2018

Stability of boundary layer flow based on energy gradient theory

The flow of the laminar boundary layer on a flat plate is studied with simulation of Navier-Stokes equations. The mechanisms of flow instability at external edge of the boundary layer and near the wall are analyzed using the energy gradient theory. The simulation results show that there is an overshoot on the velocity profile at the external edge of the boundary layer. At this overshoot, the energy gradient function is very large which results in instability according to the energy gradient theory. It is found that the transverse gradient of the total mechanical energy is responsible for the instability at the external edge of the boundary layer, which induces the entrainment of external flow into the boundary layer. Within the boundary layer, there is a maximum of the energy gradient function near the wall, which leads to intensive flow instability near the wall and contributes to the generation of turbulence.

physics.flu-dyn↗
arXiv2018

Physics of Flow Instability and Turbulent Transition in Shear Flows

In this paper, the physics of flow instability and turbulent transition in shear flows is studied by analyzing the energy variation of fluid particles under the interaction of base flow with a disturbance. For the first time, a model derived strictly from physics is proposed to show that the flow instability under finite amplitude disturbance leads to turbulent transition. The proposed model is named as "energy gradient method." It is demonstrated that it is the transverse energy gradient that leads to the disturbance amplification while the disturbance is damped by the energy loss due to viscosity along the streamline. It is also shown that the threshold of disturbance amplitude obtained is scaled with the Reynolds number by an exponent of -1, which exactly explains the recent modern experimental results by Hof et al. for pipe flow. The mechanism for velocity inflection and hairpin vortex formation are explained with reference to analytical results. Following from this analysis, it can be demonstrated that the critical value of the so called energy gradient parameter Kmax is constant for turbulent transition in wall bounded parallel flows, and this is confirmed by experiments and is about 370-389. The location of instability initiation in the flow field accords well with the experiments for both pipe Poiseuille flow (r/R=0.58) and plane Poiseuille flow (y/h=0.58). It is also inferred from the proposed method that the transverse energy gradient can serve as the power for the self-sustaining process of wall bounded turbulence. Finally, the relation of "energy gradient method" to the classical "energy method" based on Rayleigh-Orr equation is discussed.

physics.flu-dyn↗
arXiv2014

Secret Hidden in Navier-Stokes Equations: Singularity and Criterion of Turbulent Transition

A new formulation of the Navier-Stokes equation, in terms of the gradient of the total mechanical energy, is derived for the time-averaged flows, and the singular point possibly existing in the Navier-Stokes equation is exactly found. Transition of a laminar flow to turbulence must be implemented via this singular point. For pressure driven flows, this singular point corresponds to the inflection point on the velocity profile. It is found that the stability of a flow depends on the direction of the gradient of the total mechanical energy for incompressible pressure-driven flow. When this direction is nearer the normal direction of the streamline, the flow is more unstable. It is further demonstrated that the existence of the singularity in the time-averaged Navier-Stokes equation is the necessary and sufficient condition for the turbulent transition. In turbulent transition, it is observed that the role of disturbance is to promote the flow approaching to produce this singular point. These results are the most important part of the energy gradient theory.

physics.flu-dyn↗
arXiv2011

Stability of Inviscid Parallel Flows between Two Parallel Walls

In this paper, the stability of inviscid parallel flow between two parallel walls is studied. Firstly, it is obtained that the profile of the base flow for this classical problem is a uniform flow. Secondly, it is shown that the solution of the disturbance equation is cr=U and ci=0, i.e., the propagation speed of the disturbance equals the flow velocity and the disturbance in this flow is neutral. Finally, it is suggested that the classical Rayleigh Theorem on inflectional velocity instability is incorrect which states that the necessary condition for instability of inviscid parallel flow is the existence of an inflection point on the velocity profile.

physics.flu-dyn↗
arXiv2010

Energy Loss Distribution in the Plane Couette Flow and the Taylor-Couette Flow between Concentric Rotating Cylinders

The distribution of energy loss due to viscosity friction in plane Couette flow and Taylor-Couette Flow between concentric rotating cylinders are studied in detail for various flow conditions. The energy loss is related to the industrial processes in some fluid delivery devices and has significant influence on the flow efficiency, flow stability, turbulent transition, mixing, and heat transfer behaviours, etc. Therefore, it is important to know about the energy loss distribution in the flow domain and to know its influence on the flow for better understanding of the flow physics. The calculation or methodology of calculating the energy loss distribution in the Taylor-Couette flow between concentric rotating cylinders is not readily found in the open literature. In this paper, the principle and the calculation are given for single cylinder rotation of either the inner or outer cylinder, and counter and same direction rotation of two cylinders. For comparison, the distribution of energy loss in a plane Couette flow is also derived for various flow conditions. Discussions of the effect of energy loss on the flow behaviour are carried out from which some findings are suggested.

physics.flu-dyn↗
arXiv2010

Instability of Taylor-Couette Flow between Concentric Rotating Cylinders

The energy gradient theory is used to study the instability of Taylor-Couette flow between concentric rotating cylinders. This theory has been proposed in our previous works. In our previous studies, the energy gradient theory was demonstrated to be applicable for wall-bounded parallel flows. It was found that the critical value of the energy gradient parameter Kmax at turbulent transition is about 370-389 for wall-bounded parallel flows (which include plane Poiseuille flow, pipe Poiseuille flow and plane Couette flow) below which no turbulence occurs. In this paper, the detailed derivation for the calculation of the energy gradient parameter in the flow between concentric rotating cylinders is provided. The calculated results for the critical condition of primary instability (with semi-empirical treatment) are found to be in very good agreement with the experiments in the literature. A possible mechanism of spiral turbulence generation observed for counter-rotation of two cylinders can also be explained using the energy gradient theory. The energy gradient theory can serve to relate the condition of transition in Taylor-Couette flow to that in plane Couette flow. The latter reasonably becomes the limiting case of the former when the radii of cylinders tend to infinity. It is our contention that the energy gradient theory is possibly fairly universal for analysis of flow instability and turbulent transition, and is found valid for both pressure and shear driven flows in parallel and rotating flow configurations.

physics.flu-dyn↗
arXiv2010

Simulations of Detonation Wave Propagation in Rectangular Ducts Using a Three-Dimensional WENO Scheme

This paper reports high resolution simulations using a fifth-order weighted essentially non-oscillatory (WENO) scheme with a third order TVD Runge-Kutta time stepping method to examine the features of detonation front and physics in square ducts. The simulations suggest that two and three-dimensional detonation wave front formations are greatly enhanced by the presence of transverse waves. The motion of transverse waves generates triple points (zones of high pressure and large velocity coupled together), which cause the detonation front to become locally overdriven and thus form "hot spots". The transversal motion of these hot spots maintains the detonation to continuously occur along the whole front in two and three-dimensions. The present simulations indicate that the influence of the transverse waves on detonation is more profound in three dimensions and the pattern of quasi-steady detonation fronts also depends on the duct size. For a narrow duct (4LX4L where L is the half reaction length), the detonation front displays a distinctive "spinning" motion about the axial direction with a well-defined period. For a wider duct (20LX20L), the detonation front exhibits a "rectangular mode" periodically, with the front displaying "convex" and "concave" shapes one following the other and the transverse waves on the four walls being partly out-of-phase with each other.

physics.flu-dyn↗