功率超声作用下溶液温度变化的数学模拟

Mathematical Simulation of Temperature Variation of Solution Irradiated by Power Ultrasound

热效应是超声与溶液媒质相互作用的主要机制之一.为表征开放体系中超声作用下溶液温度的变化规律,以超声在流体中传播时流体对超声机械能的吸收为基础,根据化工热传递的基本原理,构建并求解了该状态下溶液体系热量衡算的微分方程,由超声参数和溶液特性参数等变量推导获得了溶液温度的数学模型.同时,通过实验研究了不同强度超声作用下磷酸盐溶液的温度变化规律,统一了不同超声作用条件下的溶液温度变化模型,并确定了相关的模型参数.经检验,关联超声波强度和作用时间的溶液主体温度方程能较好地拟合所获得的实验数据.

Thermal effect is one of major mechanisms for the interactions between power ultrasound and liquid media. In order to reveal the temperature variation of solution irradiated by power ultrasound in an open system, a differential equation describing the heat balance during the ultrasound propagation through the liquid was founded and solved based on the principles of ultrasonic energy absorption and heat transfer, and a mathematical model describing the solution temperature was derived according to the ultrasonic parameters and the solution features. Moreover, experiments were performed to reveal the temperature variation of phosphate solution irradiated by the uhrasound with various intensities, and the temperature model for the same solution irradiated by ultrasonic was united, with the parameters of the model being also determined. Tested results show that the equation describing the temperature of bulk solution, which is derived from the ultrasonic intensity and the duration of ultrasound irradiating, fits well with the experimental data.