金红石瓷无模成形技术中引发剂液滴运动的Runge-Kutta解析

分析了金红石瓷无模成形技术中,PVA-TiO2浆料胶凝前引发剂Na2B4O7·10H2O水溶液液滴的运动,建立了金属管阵列中竖直向下运动液滴的运动微分方程.在MATLAB 6.5中用四阶Runge-Kutta法求解液滴运动的常微分方程.建立了沿浆料层方向及沿浆料层法向液滴运动速度与时间及浆料层倾斜角的数学模型.研究结果表明:液滴运动速度随着时间呈二阶非线性增加,其中二次项可以定量分析空气阻力与时间的变化关系;漏斗形金属管阵列中,所有竖直向下的液滴沿平行于PVA-TiO2浆料层方向的速度分量,随着浆料层倾斜角的增加而增加,但延法向的速度分量减小;两个方向的速度随着运动时间增加均增加,同时增加空气的阻力.

Modeling on falling velocity for accelerant drops in freeform fabrication of rutile ceramic components by the Runge-Kutta method

Numerical modeling on falling of sodiumtetraborate aqueous solution drops as the accelerant before the gelation of PVA-TiO_2 suspensions in freeform fabrication of rutile ceramic components was established.Effect of time and elevation angle of the PVA-TiO_2 suspensions on the falling velocity of the sodiumtetraborate aqueous solution drops was analyzed.An ordinary differential equation for the falling drops was given.Integration of the ordinary differential equation was fulfilled using the fourth-order Runge-Kutta method in MATLAB 6.5.From the established model,a second-order nonlinear effect of time on the velocity of the drops during falling is deter- mined and the quadratic term-3.408t~2 serves as the effect of time on the air resistance.On the other hand,component of the falling velocity along the suspensions increases with the increasing of the elevation angle.However,for the component vertical to the suspen- sions,with elevation angle increasing,it decreases.