矩形通道内脉动流摩阻系数的二阶傅里叶拟合

x Second-order Fourier method to fit pulsating flow friction coefficient in rectangular channel

矩形通道内脉动流,流量的正弦脉动会引起压力的脉动,在层流区压力与正弦规律吻合良好,而在紊流区、过渡区和跨区域的压力脉动与正弦规律偏差较大.为了能够较为精确地计算管内压降,对矩形通道内脉动流进行了试验研究.通过测量截面为40 mm×3 mm的矩形通道内不同周期、振幅、平均值的正弦脉动流体的流量、压差,对压差数据分别采用一阶、二阶傅里叶级数进行拟合,发现用二阶傅里叶级数拟合压差数据,能够很好地反映压差的变化规律,并发现雷诺数-摩阻系数曲线呈‘8’字形.通过对二阶傅里叶级数的压差拟合公式进行分析、推导、拟合,得到了瞬时及平均摩阻系数的计算公式,其计算值与实验值的误差较小.

The pulsating flow in a rectangular channel and the flow rate sine fluctuation have large deviation, lead- ing to pressure drop fluctuation, and in the lamina region this fluctuation also fits the sine law well. However, while in turbulent region, transition region, and inter-regional region the pressure drop fluctuation will deviate the sine law considerably. In order to calculate the pressure drop more precisely, an experiment of pulsating flow in the rec- tangular channel was performed. Flow rate and pressure drop of different periods, amplitudes and average value of sine pulsating flow were measured in a 40 mm × 3 mm rectangular channel. First-order Fourier series and second-order Fourier series were used to fit the pressure drop data, respectively. The second-order Fourier series was found to express the pressure variation well, and the Reynolds-friction coefficient curve＇s shape looks like ‘ 8＇. The func-tions to calculate the instantaneous and average coefficient of friction resistance were derived by analyzing and fitting with the pressure drop of second-order Fourier series. The relative errors between the experimental pressure drop da-ta and the calculated results are minor.