【作者】 王浩；

【导师】 赵茉莉；

【作者基本信息】 山东大学 ， 工程力学， 2023， 硕士

【摘要】 在晶体生长、电磁冶金、热核聚变反应堆等一些工程应用中,需要通过磁场控制导电流体的流动,以达到实际生产需求。当导电流体在磁场的影响下流动时会产生感生电流,该感生电流与外置磁场的相互作用下会产生Lorenz力,从而使流场的流动特性发生改变,流场的流动稳定性也会变得难以预测。该类问题被称为磁流体力学(MHD)稳定性问题,近年来受到大量学者的关注和研究。本文以线性粘弹性的Jeffrey流体为研究对象,探讨了导电流体在饱和多孔介质中受外置静态法向磁场作用下,由水平温度梯度和浓度梯度引起的双扩散对流的发生过程。重点研究了磁场对流动稳定性的影响。本文通过线性稳定性分析和非线性稳定性分析得到流动系统临界失稳时的临界热Rayleigh数,从而对系统稳态解的稳定性进行分析。在线性稳定性分析中,采用正则模态稳定性分析方法建立了流动系统线性稳定性方程并用Chebyshev-tau方法进行数值求解。依据粘弹性流体的流动特性,线性稳定性分析分为定常对流失稳与振荡对流失稳两部分。结果表明,外置法向磁场延缓了对流失稳的开始,对流动系统的稳定有促进作用。当溶质集中在多孔层下边界时,系统首先从定常对流模式开始失稳;当溶质集中在多孔层上边界时,系统转变为振荡对流模式失稳。在振荡对流稳定性中,粘弹性流体的应力松弛时间的增加对流动稳定性具有削弱的影响,而应力弛豫时间的增加对流动稳定性具有强化作用。对比定常对流与振荡对流失稳时的临界热Rayleigh数,发生振荡对流时,流动系统的稳定性整体上有着明显的下滑。在非线性稳定性分析中,通过构造能量泛函进行非线性稳定性分析,结合打靶法与Runge-Kutta法对稳定性分析得到的特征值问题进行了数值求解。结果表明,水平方向上的温度与浓度梯度是产生亚临界不稳定性区域的主要原因。提高外置磁场的磁场强度有助于缩小亚临界不稳定性区域,并且随着Hartmann数即磁场强度的增大,通过线性稳定性分析与非线性稳定性分析得到的失稳阈值之间的差距减小。更多还原

【Abstract】 In some engineering applications,such as crystal growth,electromagnetic metallurgy,and cooling of thermonuclear fusion reactors,it is necessary to control the flow of conductive fluids through a magnetic field in order to achieve the desired production results.When the conductive fluid flows under the action of a magnetic field,induced currents are generated,which interact with an externally applied magnetic field to produce a Lorentz force,thereby causing changes in the flow cha.racteristics of the flow field.Therefore,the flow stability of the flow field becomes difficult to predict.These types of problems are known as magnetohydrodynamic(MHD)stability problems,which have received a lot of attention and research in recent years.In this paper,linear viscoelastic Jeffrey fluids were studied to investigate the occurrence of double-diffusive convection induced by horizontal temperature and concentration gradients in a conducting fluid under the action of an exte.rnally applied static normal magnetic field in a saturated porous medium.The influence of the magnetic field on flow stability was the focus of this study.The critical Rayleigh number at which the flow system becomes unstable was obtained through linear stability analysis and nonlinear stability analysis,and the stability of the system’s steady-state solution was analyzed.In the linear stability analysis,a regular mode stability analysis method was used to establish the linear stability equation of the flow system and numerical solutions were obtained using the Chebyshev-tau method.Based on the flow characteristics of viscoelastic fluids,the linear stability analysis was divided into steady convection instability and oscillatory convection instability.The results showed that the externally applied normal magnetic field delayed the onset of convection instability and promoted the stability of the flow system.When the solute was concentrated at the lower boundary of the porous layer,the system first became unstable in the steady convection mode;when the solute was concentrated at the upper boundary of the porous layer,the system transitioned to oscillatory convection instability.In the stability of oscillatory convection,increasing the stress relaxation time of viscoelastic fluids weakened the fiow stability,while increasing the retardation time strengthened the flow stability.Comparing the critical Rayleigh numbers of steady convection and oscillatory convection instability,the overall stability of the flow system was significantly reduced when oscillatory convection occurred.In the nonlinear stability analysis,a non-linear stability analysis was carried out by constructing an energy functional,and numerical solutions were obtained for the characteristic value problem obtained from the stability analysis using shooting method and Runge-Kutta method.The results showed that the temperature and concentration gradients in the horizontal direction were the main cause of the subcritical instability region.Increasing the magnetic field strength of the externally applied magnetic field helps to reduce the subcritical instability region.the magnetic field strength increases the difference between the destabilization threshold obtained through linear stability analysis and nonlinear stability analysis decreases.更多还原