流场几何突变部位力学环境的Lattice Boltzmann模拟分析
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摘要
柱体绕流和血液流动都是自然界中普遍存在的现象,它们与人类的生活密切相关,长期以来都受到众多学者的关注。在计算机出现以前,人们对此类现象的研究主要是通过理论分析和实验观测的方法来进行的,但是随着科技的发展,人们在工程中遇到的问题越来越复杂,传统的理论分析和实验观测的方法已经难以适应现代工程的需要。而计算机的出现为人们解决现代工程中的一些复杂问题开辟了一条新的途径,计算机模拟已经成为现代科学研究中的一种重要方法,为人们认识和了解一些复杂的自然现象提供了极大的帮助。在本文的工作中,我们通过计算机模拟的手段,用Lattice Boltzmann方法对方柱绕流现象和分岔血管内的血液流动现象分别进行模拟分析,力图发现并了解存在于其中的一些规律,以便对这两种流动现象有比较清晰的认识。本文的工作主要包括以下两个方面:
(1)方柱绕流的研究:对此问题的研究主要包括三个方面的工作。首先,我们模拟了位于流场中央的单个方柱绕流现象,观察了方柱的尾流在不同雷诺数条件下的变化情况,结果发现:随着雷诺数的变化,方柱的尾流呈现出两种明显不同的流动形态:当雷诺数比较小时,方柱后面只出现两个对称的漩涡但没有形成涡街,随着雷诺数的增大,两个对称漩涡会逐渐失去对称性而产生振动,形成周期性涡街。方柱的尾流从对称漩涡转变成周期性涡街的临界雷诺数大约等于60。同时我们还计算了不同雷诺数条件下方柱的Strouhal数,并与其它文献进行了比较,结果是吻合的。然后,我们对两个并列方柱的绕流现象进行了模拟分析,发现在雷诺数不变的情况下,两个方柱之间的间距对其尾流形态起着决定性的影响:当间距比较小时,两个方柱的尾流是不对称的,因为相距很近,都位于彼此可以影响到的流场范围内,相互之间会产生干扰,这种干扰是不对称的,所以两条尾流也不对称,这时两个方柱的升力系数和阻力系数相差较大,Strouhal数也有明显的波动,流场的流动表现出偏流特性;随着间距的逐渐增大,两个方柱渐渐远离,彼此之间的干扰逐渐减弱,当间距增大到某一临界值时,流场的流动形态从偏流转变成关于间距中心轴线对称的对称流,这时两个方柱有相同的阻力系数,Strouhal数也基本相等,而升力系数则关于x=0对称。流动由偏流转变成对称流的临界间距比大约为s=1.5。当s＜1.5,流动表现出偏流的特性,当s＞1.5时,流动表现出对称流的特性。在以上工作的基础上,我们进一步研究了不同间距、不同雷诺数条件下方柱的绕流特征。研究结果显示:当两个方柱的间距处于临界间距附近时(如s=1.5和1.8),随着雷诺数的增大,它们的均值升力系数和均值阻力系数有比较明显的波动。这是因为处于临界间距条件下的两个方柱,其尾流也处于由偏流转变成对称流的临界状态,这种临界状态是不稳定的,雷诺数的变化会对它产生影响:当雷诺数比较小时,两个方柱受到流场的作用接近于对称,所以它们的均值升力系数和均值阻力系数有着相同的变化趋势;随着雷诺数的增大,流场的不稳定性也随之增强,这时两个方柱在流场中的对称状态被打破,它们的均值升力系数和均值阻力系数的变化趋势不再相同,并且出现了比较明显的波动。当两个方柱的间距比临界间距大时(如s=2.5),流场已经处于对称状态,即使雷诺数的增大使流场的不稳定性增强也不足以打破两个方柱在流场中的对称状态,这时,它们的均值升力系数和均值阻力系数只是随着雷诺数的变化产生有规则的变化,而没有出现明显的波动。
(2)分岔血管内血液流动特征的研究:主要对单分岔血管、二级对称分岔血管和具有自相似结构的多分岔血管的血液流动特征进行了模拟分析。在对单分岔血管的研究中,我们主要观察了分岔附近的流动现象。因为母管和子管之间有一段扩展区域,流体流经这段区域时速度会减慢,横截面的速度剖面不再是抛物线分布,最大速度也不是在母管中心线的位置而是在靠近两边管壁的部位,母管中心线附近的流体其流速随着与分岔部位距离的缩短而逐渐减小。流体在分岔附近区域分成两股流入两根子管,子管中流体的速度剖面呈抛物线分布;在对二级对称分岔血管的研究中,我们主要分析了分岔角度对分岔附近区域流动特征的影响,发现分岔角度的增大不仅使分岔附近区域的最大流速随之增大,而且向两边管壁发生偏移。这主要是因为流体在流经分岔区域时与管壁发生碰撞,同时受到来自管壁的与其流向成一定角度的作用力,流体的速度和流向会因此而发生改变。分岔角度越大,流体的速度和流向的变化也越大,甚至会在分岔附近出现诸如二次流之类的流动现象,这时分岔附近区域的流动特征就更加复杂。在对具有自相似结构的多级分岔血管的研究中发现:流体主要在靠近中间部位的分枝内流动,两侧分枝的流速很小,流体几乎处于静止状态。随着分岔的增多,从母管到子管的平均流速其总体变化趋势是递减的,流体在整个分枝系统中的流动越来越慢,这一特征与大多数生物分枝系统的流动特征是相似的。
Flow around cylinder and blood flow in vessel,two phenomena existing extensively in nature,have attracted many researchers'attention for a long time because of their importance of human being and were studied by theoretical and experimental methods in the past.After the inventation of computer,the numerical simulation method,an indispensable method in modern research work,has been used to deal with many complex problems which are difficult to solve by theoretical and experimental methods,this method is a new way for researchers to investigate some complex phenomena.In the thesis,the flow around the square cylinder and blood flow in a vessel with bifurcation are investigated by Lattice Boltzmann method,a numerical simulation method of studying flow phenomenon,the investigation includes two fields:
(1) Flow around square cylinder.This field includes three parts:first the flow around a square cylinder placed in the center of a channel is simulated,it is found that the wake of the square cylinder presents two different patters at different Reynolds numbers:a pair of symmetrical vortices appear at small Reynolds numbers and a vortex street appear at big Reynolds numbers,the transition from symmetrical vortices to vortex street appears at Re≈60.The Strouhal numbers are also calculated at different Reynolds numbers,and they are in good agreement with published data; In the second part,the flow around two square cylinders arranged side by side is investigated at invariable Reynolds number,the results show that,the flow pattern is decided by gap ratio:the asymmetrical flow pattern occurs at small gap ratio and the symmetrical flow pattern occurs at big gap ratio,the transition of flow from asymmetrical pattern to symmetrical pattern appears at s=1.5.When s＜1.5,the flow is biased,and the two square cylinders have different lift and drag coefficients,their Strouhal numbers are fluctuant distinctly;When s＞1.5,the flow is symmetrical and the two square cylinders have equal drag coefficients and Strouhal numbers,their lift coefficients are symmetrical with x=0;In the third part,the flow is simulated at different gap ratios and different Reynolds numbers,it shows that,the time averaged lift and drag coefficients of two square cylinders are fluctuant with the increase of Reynolds number at s=1.5 and 1.8,but the fluctuations almost disappear with the increase of Reynolds number at s=2.5,this difference is induced by the difference of flow pattern.At s=1.5 and 1.8,the flow is in the critical state from biased pattern to symmetrical pattern and it is unsteady,in this situation,the increase of Reynolds number would make the two square cylinders,they are in the symmetrical state and have similar averaged lift and drag coefficients at small Reynolds numbers,in the asymmetrical state and have fluctuant averaged lift and drag coefficients;At s=2.5, the flow is in symmetrical state and it is unchanged with the increase of Reynolds numbers,in this state,the two squarec cylinders are also in the symmetrical state and have similar variable averaged lift and drag coefficients,but they are not fluctuant.
(2) Blood flow in a vessel with bifurcation.The blood flow in a vessel with one bifurcation,secondary-bifurcation and multi-bifurcation are investigated,respectively. The first investigation is about the flow in the vessel with one bifurcation,the flow characteristics near the bifurcation were observed,and the results reveal that the flow velocity decrease before entering the branches,the maximum velocity is not at the centerline of main tube but at the places near the walls.In the second investigation, the flow in the vessel with secondary-bifurcation is simulated with different bifurcation angles,it shows that the maximum velocity increase and shift towards the walls of branches with the increase of bifurcation angles as the force from the walls changing the flow velocity and its direction.In the third investigation,the flow in the self-similar veseel with multi-bifurcation is simulated,it is found that the flow running in the inner branches and almost motionless in the external branches,from the main tube to branches,the flow is slower and slower.This characteristic is similar with the flow characteristics of most biologic branch systems.
(1)方柱绕流的研究:对此问题的研究主要包括三个方面的工作。首先,我们模拟了位于流场中央的单个方柱绕流现象,观察了方柱的尾流在不同雷诺数条件下的变化情况,结果发现:随着雷诺数的变化,方柱的尾流呈现出两种明显不同的流动形态:当雷诺数比较小时,方柱后面只出现两个对称的漩涡但没有形成涡街,随着雷诺数的增大,两个对称漩涡会逐渐失去对称性而产生振动,形成周期性涡街。方柱的尾流从对称漩涡转变成周期性涡街的临界雷诺数大约等于60。同时我们还计算了不同雷诺数条件下方柱的Strouhal数,并与其它文献进行了比较,结果是吻合的。然后,我们对两个并列方柱的绕流现象进行了模拟分析,发现在雷诺数不变的情况下,两个方柱之间的间距对其尾流形态起着决定性的影响:当间距比较小时,两个方柱的尾流是不对称的,因为相距很近,都位于彼此可以影响到的流场范围内,相互之间会产生干扰,这种干扰是不对称的,所以两条尾流也不对称,这时两个方柱的升力系数和阻力系数相差较大,Strouhal数也有明显的波动,流场的流动表现出偏流特性;随着间距的逐渐增大,两个方柱渐渐远离,彼此之间的干扰逐渐减弱,当间距增大到某一临界值时,流场的流动形态从偏流转变成关于间距中心轴线对称的对称流,这时两个方柱有相同的阻力系数,Strouhal数也基本相等,而升力系数则关于x=0对称。流动由偏流转变成对称流的临界间距比大约为s=1.5。当s＜1.5,流动表现出偏流的特性,当s＞1.5时,流动表现出对称流的特性。在以上工作的基础上,我们进一步研究了不同间距、不同雷诺数条件下方柱的绕流特征。研究结果显示:当两个方柱的间距处于临界间距附近时(如s=1.5和1.8),随着雷诺数的增大,它们的均值升力系数和均值阻力系数有比较明显的波动。这是因为处于临界间距条件下的两个方柱,其尾流也处于由偏流转变成对称流的临界状态,这种临界状态是不稳定的,雷诺数的变化会对它产生影响:当雷诺数比较小时,两个方柱受到流场的作用接近于对称,所以它们的均值升力系数和均值阻力系数有着相同的变化趋势;随着雷诺数的增大,流场的不稳定性也随之增强,这时两个方柱在流场中的对称状态被打破,它们的均值升力系数和均值阻力系数的变化趋势不再相同,并且出现了比较明显的波动。当两个方柱的间距比临界间距大时(如s=2.5),流场已经处于对称状态,即使雷诺数的增大使流场的不稳定性增强也不足以打破两个方柱在流场中的对称状态,这时,它们的均值升力系数和均值阻力系数只是随着雷诺数的变化产生有规则的变化,而没有出现明显的波动。
(2)分岔血管内血液流动特征的研究:主要对单分岔血管、二级对称分岔血管和具有自相似结构的多分岔血管的血液流动特征进行了模拟分析。在对单分岔血管的研究中,我们主要观察了分岔附近的流动现象。因为母管和子管之间有一段扩展区域,流体流经这段区域时速度会减慢,横截面的速度剖面不再是抛物线分布,最大速度也不是在母管中心线的位置而是在靠近两边管壁的部位,母管中心线附近的流体其流速随着与分岔部位距离的缩短而逐渐减小。流体在分岔附近区域分成两股流入两根子管,子管中流体的速度剖面呈抛物线分布;在对二级对称分岔血管的研究中,我们主要分析了分岔角度对分岔附近区域流动特征的影响,发现分岔角度的增大不仅使分岔附近区域的最大流速随之增大,而且向两边管壁发生偏移。这主要是因为流体在流经分岔区域时与管壁发生碰撞,同时受到来自管壁的与其流向成一定角度的作用力,流体的速度和流向会因此而发生改变。分岔角度越大,流体的速度和流向的变化也越大,甚至会在分岔附近出现诸如二次流之类的流动现象,这时分岔附近区域的流动特征就更加复杂。在对具有自相似结构的多级分岔血管的研究中发现:流体主要在靠近中间部位的分枝内流动,两侧分枝的流速很小,流体几乎处于静止状态。随着分岔的增多,从母管到子管的平均流速其总体变化趋势是递减的,流体在整个分枝系统中的流动越来越慢,这一特征与大多数生物分枝系统的流动特征是相似的。
Flow around cylinder and blood flow in vessel,two phenomena existing extensively in nature,have attracted many researchers'attention for a long time because of their importance of human being and were studied by theoretical and experimental methods in the past.After the inventation of computer,the numerical simulation method,an indispensable method in modern research work,has been used to deal with many complex problems which are difficult to solve by theoretical and experimental methods,this method is a new way for researchers to investigate some complex phenomena.In the thesis,the flow around the square cylinder and blood flow in a vessel with bifurcation are investigated by Lattice Boltzmann method,a numerical simulation method of studying flow phenomenon,the investigation includes two fields:
(1) Flow around square cylinder.This field includes three parts:first the flow around a square cylinder placed in the center of a channel is simulated,it is found that the wake of the square cylinder presents two different patters at different Reynolds numbers:a pair of symmetrical vortices appear at small Reynolds numbers and a vortex street appear at big Reynolds numbers,the transition from symmetrical vortices to vortex street appears at Re≈60.The Strouhal numbers are also calculated at different Reynolds numbers,and they are in good agreement with published data; In the second part,the flow around two square cylinders arranged side by side is investigated at invariable Reynolds number,the results show that,the flow pattern is decided by gap ratio:the asymmetrical flow pattern occurs at small gap ratio and the symmetrical flow pattern occurs at big gap ratio,the transition of flow from asymmetrical pattern to symmetrical pattern appears at s=1.5.When s＜1.5,the flow is biased,and the two square cylinders have different lift and drag coefficients,their Strouhal numbers are fluctuant distinctly;When s＞1.5,the flow is symmetrical and the two square cylinders have equal drag coefficients and Strouhal numbers,their lift coefficients are symmetrical with x=0;In the third part,the flow is simulated at different gap ratios and different Reynolds numbers,it shows that,the time averaged lift and drag coefficients of two square cylinders are fluctuant with the increase of Reynolds number at s=1.5 and 1.8,but the fluctuations almost disappear with the increase of Reynolds number at s=2.5,this difference is induced by the difference of flow pattern.At s=1.5 and 1.8,the flow is in the critical state from biased pattern to symmetrical pattern and it is unsteady,in this situation,the increase of Reynolds number would make the two square cylinders,they are in the symmetrical state and have similar averaged lift and drag coefficients at small Reynolds numbers,in the asymmetrical state and have fluctuant averaged lift and drag coefficients;At s=2.5, the flow is in symmetrical state and it is unchanged with the increase of Reynolds numbers,in this state,the two squarec cylinders are also in the symmetrical state and have similar variable averaged lift and drag coefficients,but they are not fluctuant.
(2) Blood flow in a vessel with bifurcation.The blood flow in a vessel with one bifurcation,secondary-bifurcation and multi-bifurcation are investigated,respectively. The first investigation is about the flow in the vessel with one bifurcation,the flow characteristics near the bifurcation were observed,and the results reveal that the flow velocity decrease before entering the branches,the maximum velocity is not at the centerline of main tube but at the places near the walls.In the second investigation, the flow in the vessel with secondary-bifurcation is simulated with different bifurcation angles,it shows that the maximum velocity increase and shift towards the walls of branches with the increase of bifurcation angles as the force from the walls changing the flow velocity and its direction.In the third investigation,the flow in the self-similar veseel with multi-bifurcation is simulated,it is found that the flow running in the inner branches and almost motionless in the external branches,from the main tube to branches,the flow is slower and slower.This characteristic is similar with the flow characteristics of most biologic branch systems.
引文
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