不可压缩流动问题混合Galerkin型方法稳定性的数值研究

研究了求解不可压缩流动问题的混合Galerkin型方法的稳定性问题,提出了一种在混合Galerkin型方法中满足离散LBB条件的一般性方法,即速度逼近空间维数大于压力逼近空间维数,并且两个逼近空间同时连续时,离散LBB条件可以得到满足.文中以混合有限元方法和混合无单元Galerkin方法为例,通过数值实验,验证了结论的正确性.     

卡莱公司MCR引用

实践证明,将MCR控制工具应用到卡莱轮胎公司中,成功地降低了企业库存,加速了企业资金流动,具有良好的应用性。     

Numerical study of macroscopical drainage process in fabricating foamed aluminum using microscopical method

The velocity field in a single Plateau border（PB） of the aluminum foam in the drainage process is studied using a mathematical model for the flow inside a microchannel.We show that the liquid/gas interface mobility characterized by the Newtonian surface viscosity has a substantial effect on the velocity inside the single PB.With the same liquid/gas interfacial mobility and the same radius of the curvature,the maximum velocity inside an exterior PB is about 6～8 times as large as that inside an interior PB.We also find a critical value of the interfacial mobility in the interior PB.For the values greater and less than this critical value,the effects of the film thickness on the velocity in the PB show opposite tendencies.Based on the multiscale methodology,with the coupling between the microscale and the macroscale and the results obtained from the microscopical model,a simplified macroscopical drainage model is presented for the aluminum foams.The comparisons among the computational results obtained from the present model,the experimental data quoted in the literature,and the results of the classical drainage equation show a reasonable agreement.The computational results reveal that the liquid holdup of the foams is strongly dependent on the value of the mobility and the bubble radius.     

Series solutions for the stagnation flow of a second-grade fluid over a shrinking sheet

This study derives the analytic solutions of boundary layer flows bounded by a shrinking sheet. With the similarity transformations, the partial differential equations are reduced into the ordinary differential equations which are then solved by the homotopy analysis method （HAM）. Two-dimensional and axisymmetric shrinking flow cases are discussed.     

Basic function scheme of polynomial type

A new numerical method named as basic function method is proposed. It can directly discretize differential operators on unstructured grids. By expanding the basic function to approach the exact function, the central and upwind schemes of derivative are constructed. By using the second-order polynomial as a basic function and applying the flux splitting method and the combination of central and upwind schemes to suppress non-physical fluctuation near shock waves, a second-order basic function scheme of polynomial type is proposed to solve inviscid compressible flows numerically. Numerical results of typical examples for two-dimensional inviscid compressible transonic and supersonic steady flows indicate that the new scheme has high accuracy and high resolution for shock waves. Combined with the adaptive remeshing technique, satisfactory results can be obtained.     

Multiphase fluid dynamics and transport processes of low capillary number cavitating flows

To better understand the multiphase fluid dynamics and associated transport processes of cavitating flows at the capillary number of 0.74 and 0.54, and to validate the numerical results, a combined computational and experimental investigation of flows around a hydrofoil is studied based on flow visualizations and time-resolved interface movement. The computational model is based on a modified RNG k-ε model as turbulence closure, along with a vapor-liquid mass transfer model for treating the cavitation process. Overall, favorable agreement between the numerical and experimental results is observed. It is shown that the cavi- tation structure depends on the interaction of the water-vapor mixture and the vapor among the whole cavitation stage, the interface between the vapor and the two-phase mixture exhibits substantial unsteadiness. And, the adverse motion of the interface relates to pressure and velocity fluctuations inside the cavity. In particular, the velocity in the vapor region is lower than that in the two-phase region.     

Euler solution using adaptive Cartesian grid with a gridless boundary treatment

A quadtree-based adaptive Cartesian grid generator and flow solver were developed. The grid adaptation based on pressure or density gradient was performed and a gridless method based on the least-square fashion was used to treat the wall surface boundary condition, which is generally difficult to be handled for the common Cartesian grid. First, to validate the technique of grid adaptation, the benchmarks over a forward-facing step and double Mach reflection were computed. Second, the flows over the NACA 0012 airfoil and a two-element airfoil were calculated to validate the developed gridless method. The computational results indi- cate the developed method is reasonable for complex flows.     

Numerical investigation on the flowfield of ＂swallowtail＂ cavity for supersonic mixing enhancement

A ＂swallowtail＂ cavity for the supersonic combustor was proposed to serve as an efficient flame holder for scramjets by enhancing the mass exchange between the cavity and the main flow. A numerical study on the ＂swallow- tail＂ cavity was conducted by solving the three-dimensional Reynolds-averaged Navier-Stokes equations implemented with a k-e turbulence model in a multi-block mesh. Turbu- lence model and numerical algorithms were validated first, and then test cases were calculated to investigate into the mechanism of cavity flows. Numerical results demonstrated that the certain mass in the supersonic main flow was sucked into the cavity and moved spirally toward the combustor walls. After that, the flow went out of the cavity at its lateral end, and finally was efficiently mixed with the main flow. The comparison between the ＂swallowtail＂ cavity and the conventional one showed that the mass exchanged between the cavity and the main flow was enhanced by the lateral flow that was induced due to the pressure gradient inside the cavity and was driven by the three-dimensional vortex ring generated from the ＂swallowtail＂ cavity structure.     

高超声速激波风洞研究进展

回顾了高超声速激波风洞的研制与发展,并依据高超声速实验研究对地面实验模拟技术的要求,分别介绍了应用轻气体、自由活塞和爆轰驱动技术研制的主要激波风洞的性能、特点和存在问题.重点介绍了爆轰驱动高焓激波风洞的3种主要运行模式:反向、正向爆轰驱动与双爆轰驱动. 根据这些运行模式的工作原理,分析了应用这些驱动技术产生的高温、高压气源的特点,探讨了不同驱动技术可能影响激波风洞性能的关键问题与解决方法.目前发展的激波风洞已经能够用于开展马赫数3$\sim$30的高超声速流动的试验模拟研究,但是试验气流的品质还不能满足高超声速科技研究的需求.为了获得可靠的实验结果, 通过不断改进、完善、提高激波风洞的性能,尽可能复现高超声速飞行条件是今后主要的研究方向.      

壁流动中的转捩

对壁流动的不同实验结果做了对比,这些实验结果来自于流动显示、热膜测量以及PIV测量, 对比的同时,还总结了与此相应的理论方面的进展.这些进展是在对所选大约120篇文献中内容归纳提炼的基础上给出的.尽管实验中所使用的初始扰动条件不同,但所发现的流动结构几乎是完全一样的. 在对壁流动转捩的认识方面,认为下列所观察到的流动结构是最基本最重要的:在边界层和管流中被称为类孤子相干结构(SCS)的三维非线性涡包、$\Lambda$涡、二次涡环和涡环链.近期的实验中发现了这些结构形成和转捩的动力学过程,具体包括以下内容: (1) $\Lambda$ 涡和二次涡环间持续的相互作用过程.该过程决定了涡环链的产生方式, 总是从壁面区域周期性地形成,并进入到边界层的外部区域; (2)高频涡的生成,这是理解转捩和湍流边界层(以及其他流动)发展的关键问题之一.尽管已经提出了一些解释,但是二次涡环的实验发现将对此提供一个特别清晰的解释.(3)在所有湍流猝发中SCS所起的关键作用.这一点被看做是低雷诺数湍流边界层中湍流产生的关键机制.与猝发直接相关联的是低速条带. 基于SCS的动力学过程, 针对壁流动情况,可以比以前更清晰地解释低速条带的形成机制及其与流动结构的关系.在实验中所观察到的SCS和二次涡环,不仅能使我们重温壁面流动转捩中的经典故事, 同时还开辟一条新的途径,可以基于此建立壁面流动转捩可能具有的普适性的动力学过程.