Zhu Keqin

An analysis of a wire-plate electrostatic precipitator

Abstract A zero flux boundary condition is presented for the particle turbulent mixing diffusion equation in a wire-plate electrostatic precipitator. Since the wire-plate electrostatic precipitator is symmetric along the wire plane, only half of the symmetric plane is analyzed. This paper presents the zero flux boundary condition for the turbulent mixing diffusion model at the wire plane of a wire-plate electrostatic precipitator, ∂ C /∂ y =0 at y =0 instead of the traditional form which is E y (∂ C /∂ y )− wC =0. The improved boundary condition is validated by comparing the theoretical results with experimental data [Salcedo & Munz, (1978), Proceedings of the Third International Conference on Electrostatic Precipitation, Abano-Padova, Italy, pp. 343–359]. The zero flux boundary condition provides better results than that of the traditional form [Leonard, Mitchner, & Self (1980), Atmos. Environ. 14, 1289].

Dual Role of Wall Slip on Linear Stability of Plane Poiseuille Flow

The linear stability of plane Poiseuille flow is extended to the cases of two wall boundaries maintaining different slip coefficients β1 and β2. We determine the slip coefficient pairs, β1c and β2c, which yield the same critical Reynolds number as the classical no-slip case. It is found that the wall slip may stabilize the flow for β1 > β1c and β2 > β2c, whereas slightly destabilize the flow for β1 < β1c and β2 < β2c.

Mechanical Analogies of Fractional Elements

A Ffactional element model describes a special kind of viscoelastic material. Its stress is proportional to the fractional-order derivative of strain. Physically the mechanical analogies of fractional elements can be represented by spring-dashpot fractal networks. We introduce a constitutive operator in the constitutive equations of viscoelastic materials. To derive constitutive operators for spring-dashpot fractal networks, we use Heaviside operational calculus, which provides explicit answers not otherwise obtainable simply. Then the series-parallel formulas for the constitutive operator are derived. Using these formulas, a constitutive equation of fractional element with 1/2-order derivative is obtained. Finally we find the way to derive the constitutive equations with other fractional-order derivatives and their mechanical analogies.

Characteristics of electrorheological fluid flow in journal bearings

Under the influence of an applied electric field, the variation of apparent viscosity of electrorheological (ER) fluid flow causes ER effects. According to the Bingham model, which is widely used for describing the rheological properties of ER fluids, this variation should be very weak at high shear rates. To clarify the ER effects in ER journal bearings at high shear rate, a numerical study is presented. It is found that under the influence of the applied electric field, ER effects in ER journal bearings can be affected by not only the apparent viscosity of ER fluids but also the movement of yield surface in the clearance of ER journal bearing. In the case of low shear rate, both are effective on the lubricant film pressure of ER journal bearings. In the case of high shear rates, the main factor is the extension of non-yield region in the bearing clearance.

Characteristics of Electrorheological Fluid Flow Between Two Concentric Cylinders

The characteristics of Couette flow of electrorheological fluid (ERF) between concentric cylinders is dependent on the parameter β, which is in the yield stress formula of ERF. In the case of β > 2, the yield region locates between the yield surface and the outer cylinder. In the case of β < 2, the yield region locates between the yield surface and the inner cylinder. When β = 2, there is no yield surface. Steady and time dependent numerical results in relation to different β are presented and discussed.

Investigation of Resistivity of Saturated Porous Media with Lattice Boltzmann Method

The lattice Boltzmann method is employed to study the electrical transport properties of saturated porous media. Electrical current flow through the porous media is simulated and the relationship between resistivity index and water saturation is derived. It is found that this kind of relation is not a straight line as described by the Archie equation with the parameter n being a constant in a log–log scale. A new equation is thus developed to formulate this relation with n being a function of porosity and water saturation. The comparisons between the results by lattice Boltzmann and by the laboratory experiments on rock samples demonstrate that this numerical method can provide an alternative way for the expensive laboratory experiments to investigate the electrical transport properties of saturated porous media and can be used to explore micro mechanisms more conveniently.

Features of the supercritical transition in the wake of a circular cylinder

The features of the wake behind a uniform circular cylinder atRe=200, which is just beyond the critical Reynolds number of 3-D transition, are investigated in detail by direct numerical simulations by solving 3-D incompressible Navier-Stokes equations using mixed spectral-spectral-element method. The high-order splitting algorithm based on the mixed stiffly stable scheme is employed in the time discretization. Due to the nonlinear evolution of the secondary instability of the wake, the spanwise modes with different wavelengths emerge. The spanwise characteristic length determines the transition features and global properties of the wake. The existence of the spanwise phase difference of the primary vortices shedding is confirmed by Fourier analysis of the time series of the spanwise vorticity and attributed to the dominant spanwise mode. The spatial energy distributions of various modes and the velocity profiles in the near wake are obtained. The numerical results indicate that the near wake is in 3-D quasi-periodic laminar state with transitional behaviors at this supercritical Reynolds number.

Limit Cycles near Stationary Points in the Lorenz System

The limit cycles in the Lorenz system near the stationary points are analysed numerically. A plane in phase space of the linear Lorenz system is used to locate suitable initial points of trajectories near the limit cycles. The numerical results show a stable and an unstable limit cycle near the stationary point. The stable limit cycle is smaller than the unstable one and has not been previously reported in the literature. In addition, all the limit cycles in the Lorenz system are theoretically proven not to be planar.

Dual Role of Viscosity During Start-Up of a Maxwell Fluid in a Pipe

Based on the exact solution of start-up flow of Maxwell fluids in a long circular straight pipe, the effect of viscosity on the time of flow establishment is analysed. It is found that the viscosity of Maxwell fluids plays a dual role. A key parameter is the dimensionless relaxation time . For 0 0.0432, the viscosity mainly plays a role of strengthening the oscillation, and the time of flow establishment increases with the incremental viscosity.

Role of Viscosity Stratification and Insoluble Surfactant in Instability of Two-Layer Channel Flow

We study, for the case of the two layer plane Poiseuille flow, the effect of viscosity stratification and interfacial surfactant on the flow instability. Considering a normal mode of the streamwise wave number α, both the linear and energy analyses are presented. The expressions of perturbation energy supplied at the interface are derived. The result demonstrates that the jumps of horizontal velocity and tangential stress of the perturbed flow across the interface could be induced by the presence of viscosity stratification and surfactant. This is expected to be responsible for the Yih and Marangoni instability.