非牛顿钻井流体流动计算机智能解析方法

钻井液体在环形钻杆空间中的运动,可归结为幂律流体管内流动和螺旋流动。由于幂律流体的本构方程,在运动方程中产生速度梯度的非线性项,求解过程比较复杂。因此应用计算机符号运算、改进的Kantorovich变分法和幂律流体模型相结合,并采用局部线性化的方法,提出了解决运动方程中出现的非线性问题的方法,即计算智能解析方法应用于非线性问题,研究了幂律流体管内非定常流动,研究方法及其结果可以推广到幂律流体螺旋流动情形。     

Research advances of un-symmetric constitutive theory of anisotropic viscoelastic liquids and its hydrodynamic behavior

Research advances of un-symmetric constitutive equation of anisotropic fluid,influence of un-symmetric stress tensor on material functions,vibrational shear flow of the fluid with small amplitudes and rheology of anisotropic suspension were reported.A new concept of simple anisotropic fluid was introduced.On the basis of anisotropic principle,the simple fluid stress behaviour was described by velocity gradient tensor F and spin tensor W instead of velocity gradient tensor D in the classic Leslie-Ericksen continuum theory.Two relaxation times analyzing rheological nature of the fluid and using tensor analysis a general form of the constitutive equation of co-rotational type was introduced.More general model LCP-H for the fluid was developed.The unsymmetry of the shear stress was predicted by the present continuum theory for anisotropic viscoelastic fluid-LC polymer liquids.The influence of the relaxation times on material functions was specially studied.It is important to study the unsteady vibrational rotating flow with small amplitudes,as it is a best way to obtain knowledge of elasticity of the LC polymer,i.e.dynamic viscoelasticity.For the shear-unsymmetric stresses,two shear stresses were obtained thus two complex viscosities and two complex shear modulus(i.e.first and second one) were introduced by the constitutive equation which was defined by rotating shear rate introduced by author.For the two stability problems of fluid,such as stability of hydrodynamic flow and orientational motion,were discussed.The results show that the polymer suspension systems exhibit anisotropic character.The PNC systems can exhibit significant shear-thinning effects.For more concentrated polymer nano-suspensions,the first normal stress difference change from positive to negative,which is similar to LC polymer behavior.     

计算机智能解析方法及在非牛顿流体力学中应用

符号运算或解析处理,是当代人工智能科学的重要分支。本文简要地介绍了计算机软件Macsyma, Mathematica等的主要功能,这些软件是完成符号运算的有力工具。符号运算,计算方法和力学、流变模型相结合,提出了计算机智能解析方法。作为符号运算应用和计算解析方法应用实例,研究了Oldroyd B流体(或上随体Jeffrey流体)依时性旋转流动。文中列举了该问题的K级近似方程及其Macsyma程序,表明符号运算应用成功。     

Vibrational shear flow of anisotropic viscoelastic fluid with small amplitudes

Using the constitutive equation of co-rotational derivative type for anisotropic viscoelastic fluid-liquid crystalline(LC),polymer liquids was developed.Two relaxation times are introduced in the equation:λn represents relaxation of the normal-symmetric stress components;λs represents relaxation of the shear-unsymmetric stress components.A vibrational rotating flow in gap between cylinders with small amplitudes is studied for the anisotropic viscoelastic fluid-liquid crystalline polymer.The time-dependent constitutive equation are linearized with respect to parameter of small amplitude.For the normal-symmetric part of stress tensor analytical expression of the shear stress is obtained by the constitutive equation.The complex viscosity,complex shear modulus,dynamic and imaginary viscosities,storage modulus and loss modulus are obtained for the normal-symmetric stress case which are defined by the common shear rate.For the shear-unsymmetric stress part,two shear stresses are obtained thus two complex viscosities and two complex shear modulus(i.e.first and second one) are given by the constitutive equation which are defined by rotating shear rate introduced by author.The dynamic and imaginary viscosities,storage modulus and loss modulus are given for each complex viscosities and complex shear modulus.Using the constituive equation the rotating flow with small amplitudes in gap between two coaxial cylinders is studied.     

应用谱方法研究管内非牛顿流体的非定常流动

本文研究上随体Maxwell流体在水平管内的非定常流动,该问题可归纳为无量纲速度分量的二阶偏微分方程的边初值问题,采用以Chebyshev多项式为基底的谱方法,将该偏微分方程化为二阶常微分方程组的初值问题,采用Laplace变换,求得二阶常微分方程组的解析解。文中提出了用谱方法解非定常流动的新方法,并通过在常压力梯度和周期性压力梯度两种情形下的计算结果,与用差分法和Kantorovich变分法求得的结果进行比较,证明谱方法适合于研究非定常流动。