On the global well‐posedness for the two‐dimensional Boussinesq equations with horizontal dissipation

In this paper, we study the global well‐posedness for the two‐dimensional nonlinear Boussinesq equations with horizontal dissipation. The method we adopted is the smoothing effect in horizontal direction and the low‐high decomposition technique.     

Effects of mesoscale eddies on the spatial coherence of a middle range sound field in deep water

Mesoscale eddies have a remarkable influence on the underwater sound field. Many previous studies have investigated the effects of eddies on transmission loss, the convergence zone, time delay, etc. However, the effects of eddies on spatial coherence are less well studied and remain unclear. In this paper, the effects of eddies on spatial coherence at the subsurface in deep water are investigated. The eddy environments are simulated with Gaussian eddy equations, the complex pressure field is obtained using a range-dependent parabolic equation model and the associated mechanism is analyzed based on ray theory and models. The results show that cold/warm mesoscale eddies affect spatial coherence in a high-intensity zone by changing the locations and width of the convergence zone. In the shadow zone, the horizontal correlation radius and the vertical correlation radius increase with range and decrease with depth, and they are increased by warm eddies and decreased by cold eddies, mainly caused by variation of the multipath structure.     

Slip flow due to a stretching cylinder

The slip flow due to a stretching cylinder is studied. A similarity transform reduces the Navier-Stokes equations to a set of non-linear ordinary differential equations. Asymptotic solutions for large Reynolds number and small slip show the problem can be related to the existing two-dimensional stretching cases. Due to algebraic decay, the equations are further transformed through a compressed variable, and then integrated numerically. It is found that slip greatly reduces the magnitudes of the velocities and the shear stress.     

TR-PIV measurement of the wake behind a grooved cylinder at low Reynolds number

A comparative study of the wakes behind cylinders with grooved and smooth surfaces was performed with a view to understand the wake characteristics associated with the adult Saguaro cacti. A low-speed recirculation water channel was established for the experiment; the Reynolds number, based on the free-stream velocity and cylinder diameter (D), was kept at Re_D=1500. State-of-the-art time-resolved particle image velocimetry (TR-PIV) was employed to measure a total of 20 480 realizations of the wake field at a frame rate of 250 Hz, enabling a comprehensive view of the time- and phase-averaged wake pattern. In comparison to the wake behind the smooth cylinder, the length of the recirculation zone behind the grooved cylinder was extended by nearly 18.2%, yet the longitudinal velocity fluctuation intensity was considerably weakened. A global view of the peaked spectrum of the longitudinal velocity component revealed that the intermediate region for the grooved cylinder, which approximately corresponds to the transition region where the shear layer vortices interact, merge and shed before the formation of the Karman-like vortex street, was much wider than that for the smooth one. The unsteady events near St=0.3-0.4 were detected in the intermediate region behind the grooved cylinder, but no such events were found in the smooth cylinder system. Although the formation of the Karman-like vortex street was delayed by about 0.6D downstream for the grooved cylinder, no prominent difference in the vortex street region was found in the far wake for both cylinders. The Proper Orthogonal Decomposition (POD) method was used extensively to decompose the vector and swirling strength fields, which gave a close-up view of the vortices in the near wake. The first two POD modes of the swirling strength clarified the spatio-temporal characteristics of the shear layer vortices behind the grooved cylinder. The small-scale vortices superimposed on the shear layers behind the grooved cylinder were found to be generated and convected downstream in the same phase, which would significantly reduce the fluctuating force on the cylinder surface.     

Experimental investigation on resistance characteristics in micro/mini cylinder group

Friction factors associated with forced flow of de-ionized water over staggered and in-line micro/mini cylinder group plates with 3.5 mm width and 40 mm length, which are made of micro/mini cylinders with hydraulic diameter of 0.5 mm and the heights of 1.0 mm, 0.75 mm, 0.5 mm and 0.25 mm, respectively, have been experimentally investigated over Reynolds number ranging from 25 to 800. The flux and the pressure drop between the inlet and the outlet of micro/mini cylinder group are measured and the experimental results are compared with those of convectional correlations. The investigation shows the value of fRe is approximately the constant in micro/mini cylinder group plates when the flow is purely laminar state. Except test sections with 0.25 mm cylinder height, the values of fRe for other test sections increase when Re > 100, as the results of the appearance of vortex resistance, the enhancement of stream pulse and the acceleration of stream frequency. For test section with 0.25 mm cylinder height, the values of fRe rapidly and oscillatingly increase at Re > 150 due to the influence of the scale effect, tip clearance effect and the roughness effect on the cylinder surface and bottom of micro/mini cylinder group plates. The friction factor in a staggered array is much larger than that at in-line array for micro/mini cylinder group plates and the higher the cylinder height is, the lower the friction factor becomes.     

Optimization of clamping force for low-viscosity polymer injection molding

Due to its low cost and high efficiency, injection molding is used for the mass production of many plastic products nowadays. However, when processing low-viscosity plastic materials, i.e., materials with an excellent fluidity, an inappropriate setting of the clamping force often results in a poor appearance and dimensional accuracy of the final product. Thus, operators usually take the upper limit of the clamping force as a default in setting up the machine in an attempt to improve the quality of the molded parts. However, such an approach shortens the machine and mold life, increases the energy consumption, and leads to poor air venting. Consequently, more scientific methods for determining the clamping force setting are required. To meet this demand, the present study proposes a clamping force search methodology for determining the optimal clamping force setting of a hydraulic cylinder clamping injection molding machine in the processing of low-viscosity plastics such as thermoplastic polyurethane (TPU) and polypropylene (PP). Based on the characteristic extracted from the sensing tie-bar elongation profile under different clamping force settings, a regression analysis on these data points is implemented to seek for an optimal clamping force. The experimental results show that for an injection molding machine with a hydraulic cylinder clamping mechanism, the effect of the mold temperature on the clamping force is sufficiently small to be ignored, which has an impact on the toggle type clamping unit. Furthermore, compared to traditional methods, the optimal clamping force obtained using the method proposed in the present study results in a significant improvement in the yield rate. Overall, the results confirm that for low-viscosity polymer resins, the optimal clamping force determined using the proposed method results in a higher and more consistent quality of the molded parts than that achieved using the proper clamping force setting for ordinary-viscosity resins.     

Wave propagation through a dielectric layer containing densely packed fibers

This paper presents the theoretical formulation for the propagation of electromagnetic wave through a dielectric layer containing a random dense distribution of fibers. The diameter of the fibers is comparable to the inter-fiber spacing and wavelength of the incident radiation, but is much smaller than the thickness of the layer. Discontinuity of refractive index across the boundaries of the dielectric layer resulted in multiple internal reflection of both the primary source wave and the scattered waves. As a result the incident waves on the fibers consist of the multiply-reflected primary waves, scattered waves from other fibers, and scattered-reflected waves from the boundaries. The effective propagation constant of the dielectric fiber layer was developed by utilizing the Effective field-Quasicrystalline approximation. The influence of the refractive index of the dielectric medium on the radiative properties of a dense fiber layer was examined by means of numerical analyses.     

天文导航航向误差的数理分析

天文导航的航向误差与水平基准、载体位置的精度密切相关,以天文导航三角形的物理意义分析了天文导航测定航向的原理,推导了天文导航测定航向的精度与水平基准误差、载体地理位置误差等环节之间的公式,为天文导航仪器选择测量天体和提高精度提供了理论依据.     

Analysis of dual-phase-lag heat conduction in cylindrical system with a hybrid method

The dual-phase-lag heat transfer model is applied to investigate the transient heat conduction in an infinitely long solid cylinder for an exponentially decaying pulse boundary heat flux and for a short-pulse boundary heat flux. A hybrid application of the Laplace transform method and the control volume scheme is used to obtain the numerical solutions. Comparison between the numerical results and the analytic solution for an exponentially decaying heat flux pulse evidences the accuracy of the present numerical results. Results further show that the present numerical scheme can overcome the mathematical difficulties to analyze such problems. Effects of the thermal lag ratio τ_q/τ_T, the shift time τ_q–τ_T, the function form of heating pulse, and geometry of medium on the behavior of heat transfer are investigated.