恒定微压下微小流量的非定常流测量方法

Non-steady Flow Method for Measuring the Micro Flow at Constant Micropressure

为了精确测量微小流道中的微小流量,提出了用非定常流等效定常流进行恒定微压下微小流量测量的新方法,推导出了非定常流等效定常流进行微小流量测量时的水头适用条件。利用流体力学拉格朗日积分建立非定常流的非线性微分方程,用Matlab软件对非线性微分方程进行了数值解析,得出该测量方法的理论误差,数值结果表明在不考虑测试管段沿程阻力的条件下,被测试件过流面积与测试管断面积比值越小,非定常流与定常流条件下的测量结果差别越小。依据所提出的测量方法建立微小流量非定常流测量装置,实测结果与理论计算结果吻合良好。计算和试验表明:在满足水头适用条件且被测试件过流面积与测试管断面积比值小于3.422%时,非定常流测量方法测试精度可保证在2.27%以内。

In order to measure the micro flow in micro channel precisely and easily, a new measuring method based on the idea of utilizing non-steady flow state to be equivalent to steady flow state used in traditional measurement is proposed. The applicable condition of pressure head for the new measuring method is derived. Based on Lagrange integral principle in fuid dynamics, a mathematic model in form of non-linear differential equation is built and analyzed numerically by using MATLAB software, so the theoretical error of the proposed method is obtained. The numerical results reveal that the difference between measurement result under the non-steady flow state and that under the steady flow state reduces with the decreasing of the ratio of the areas of the micro channel and the tube in upper stream when the pressure loss in the tube is omitted. Then, an apparatus for measuring the micro flow is established according to the proposed method. The measured results from the apparatus agree well with the theoretical calculation results. Both results show that the measuring error is lower than 2.27% when the applicable condition of pressure head is satisfied and the ratio of cross sectional areas of the micro channel and the tube in upper stream is smaller than 3.422%.