Closed-Form Non-Stationary Solutionsfor Thermo and Chemovibrational Viscous Flows
Closed-Form Non-Stationary Solutionsfor Thermo and Chemovibrational Viscous Flows
复制标题
热流和化学振动粘性流的闭式非平稳解
作者：
D. Bratsun;V. Vyatkin
讨论了用Boussinesq近似表示的Navier-Stokes方程的一类闭式精确解。解描述了非均匀反应流体在低频或有限频率的简谐振动下的运动。介质的不均匀性是由于横向密度梯度而产生的，而横向密度梯度是由于反应的放热和化学转变而出现的。归根结底，流体运动的物理机制是可变惯性场对不同密度的层流亚层的不同影响。我们导出了几个热振动对流和化学振动对流问题的解，这些问题包括在平面层或封闭管内生热流体的粘性流动，以及在简谐振动下按一阶化学方案反应的流体的粘性流动。对于每种情况，都导出了流体速度、压力、温度和试剂浓度的封闭形式的解析表达式。讨论了求其精确解的一般方法。
A class of closed-form exact solutions for the Navier–Stokes equation written in the Boussinesq approximation is discussed. Solutions describe the motion of a non-homogeneous reacting fluid subjected to harmonic vibrations of low or finite frequency. Inhomogeneity of the medium arises due to the transversal density gradient which appears as a result of the exothermicity and chemical transformations due to a reaction. Ultimately, the physical mechanism of fluid motion is the unequal effect of a variable inertial field on laminar sublayers of different densities. We derive the solutions for several problems for thermo- and chemovibrational convections including the viscous flow of heat-generating fluid either in a plain layer or in a closed pipe and the viscous flow of fluid reacting according to a first-order chemical scheme under harmonic vibrations. Closed-form analytical expressions for fluid velocity, pressure, temperature, and reagent concentration are derived for each case. A general procedure to derive the exact solution is discussed.