Application of orthogonal collocations to some transport phenomena problems in co-axial cylinders and spheres

Collocation methods are developed for the solution of some differential equation models for transport phenomena problems in one-and two-dimensions in co-axial annuli of spherical and cylindrical shapes. General formulae are developed to obtain orthogonal polynomials over an arbitrary interval using two types of weighting functions. The convergence and accuracy of the methods are demonstrated using two test problems, i.e., calculation of effectiveness factors in (a) a spherical pellet with peripherally deposited catalyst and (b) a Raschig ring type cylindrical catalyst pellet. Comparisons of results obtained from the present methods with analytic solutions for the first-order reactions indicate good agreement. Numerical solutions are also obtained for the second-and the third-order reactions for which analytic solutions are not available. Results obtained in terms of a new Thiele modulus involving the ratio of volume of peripherally deposited part of catalyst to exterior surface area indicate that this normalization brings effectiveness factor versus Thiele modulus curves close together for co-axial spherical and long cylindrical pellets, as it does for these geometries without the inner co-axial portion.     

竖直圆环形通道内充分发展自然对流的分析解

对于均匀加热的竖直圆环形通道内的充分发展自然对流换热问题，发现了前人分析解不完善的地方，通过运用能量守衡原理得到了封闭形式的分析解并给出了其计算实例。在一个壁面恒热流、另一个壁面绝热的两类热边界条件下，分析解所计算得到的充分发展段的发热壁面温度与实验结果都符合得较好。最后，筒述了此分析解存在的误差以及可能产生此误差的原因。     

计算窄间隙环空循环压耗的新模型

影响窄环空中摩擦压降的关键因素为环空尺寸的变化、钻柱旋转及偏心。用Herschel—Bulkley模式描述钻井液的流变性，考虑钻柱偏心和旋转对钻井液在环空和钻柱内流动的影响，提出了一种新的计算窄间隙环空循环压耗的模型，将所建立模型和传统方法的计算结果与实测数据比较表明，该模型具有较高的精度，可以满足现场作业的要求。     

非Newton流体在内管做轴向往复运动的偏心环空中非定常流的速度分布

本文建立了双极坐标系下非Newton流体在内管做轴向往复运动的偏心环空中非定常流的控制方程；并以HPAM水溶液为例，用有限差分法对控制方程进行了数值求解，绘制了这种流动的速度分布曲线；分析了环空内外管的偏心距、环空内管的冲程和冲次对流体在偏心环空中速度分布的影响。分析结果表明：随着环空偏心距减小，最宽和最窄间隙处的流体速度分布越来越接近；随着环空内管的冲程和冲次的增加，环空内管的轴向往复运动对流体速度分布的扰动增大。     

幂律流体偏心环空螺旋流中的二次流问题

本文建立了幂律流体偏心环空螺旋流的控制议程，并用有限差分法对其数值求解。结果表明：幂律流体偏心环空螺旋流中存在二次流动、最后，还对这种二次流做了分析。     

环形窄缝通道单相流动特性研究

对环形窄缝通道内单相流动特性进行了分析，提出了理论模型预测环形窄缝通道内单相流动阻力特性。根据该模型，对窄缝宽度分别为1.0、1.5、2.0mm环形通道内单相湍流流动摩擦阻力系数进行了理论计算，并与实验结果进行了比较。理论预测值与实验结果符合较好，且窄缝间隙大小对环形窄缝通道内流动特性有着重要影响，随着间隙的减小，摩擦阻力系数相应减小。间隙对流动阻力系数的影响还依赖于Re大小，其影响随Re的减小而降低。     

窄环隙流道内自然对流沸腾换热实验研究

以水为工质 ,在常压下对竖直和倾斜环隙流道进行了自然对流沸腾换热实验研究 ,给出并讨论了间隙大小、热负荷、倾角和表面张力对换热性能的影响 ,可视化观察加深了对窄小空间沸腾现象的认识。在实验的基础上 ,提出了一个新的、可以较方便使用的传热计算关联式。     

Viscoplastic fluid flow in irregular eccentric annuli due to axial motion of the inner pipe

Fully developed axial laminar flow of viscoplastic Herschel-Bulkley fluids in eccentric annuli between two pipes has been investigated numerically. The pipes are closed at one end and flow is due to the axial motion of the inner pipe. The annuli may be filly open or partially blocked. General non-orthogonal, boundary-fitted curvilinear coordinates have been used to accurately model the irregular annular geometry due to the presence of a flow blockage. A computer code has been developed using a second-order finite-difference scheme. An exponential model for the shear stress, valid for both yielded and unyielded regions of the flow, is used in the computation. The effects of generalized Bingham number, flow behavior index, eccentricity, and blockage height on the pressure gradient or the surge pressure have been studied and the results are presented in dimensionless form. The pressure gradient is found to decrease with increasing eccentricity. For a partially blocked eccentric annulus the pressure gradient is found to decrease with an increase in the blockage height.     

STUDIES OF MIXING IN A CONCENTRIC TUBE AIR-LIFT REACTOR CONTAINING XANTHAN GUM BY MEANS OF AN IMPROVED FLOW FOLLOWER

The influence of a pseudoplastic non-Newtonian fluid upon the hydrodynamic performance and mixing parameters of a concentric tube air-lift fermenter has been studied using a range of dilute xanthan gum solutions (0-0.5% weight by volume). Liquid circulation times vary in a complex pattern with increasing gum concentration. At low concentrations, circulation was more; rapid due to drag reduction whilst at the highest concentrations circulation times were increased. The column voidage decreased with increasing gum concentration and bubbly flow in the riser was replaced by slug flow. For all gum concentrations the effective dispersion coefficient for a single passage around the loop was increased relative to tap water. An improved radio-pill flow follower system for hydrodynamic studies is described.