标量图像测速原理及数值检验

标量图像测速是一种新型的能够测量微小结构的湍流实验测量系统，其理论依据是Schmidt（Sc）数〉1的标量湍流里，标量场脉动的时间尺度和空间耗散尺度要小于对应的速度场脉动的时间尺度和空间耗散尺度，标量脉动比速度脉动具有更强的间歇性，标量场所含信息大于速度场所含信息，从高＆数标量场提取速度场是可能的。笔者详细介绍了标量图像测速原理，并在积分最小化法思想指导下根据标量输运守恒方程及限定条件，建立了积分最小化标量图像测速的数学表示。通过变分法，获得了积分空间每个点的三个速度分量的欧拉特征方程，对欧拉特征方程离散化即可在积分空间建立一线性稀疏方程组。采用变分迭代法对此线性稀疏方程组进行求解即可获得三维速度场，据此采用积分最小化法建立了标量图像测速图像处理系统。还介绍了四维标量场（三维空间加一维时间）的图像采集原理，并采用DNS数据对标量图像测速处理系统进行了数值检验，检验结果表明标量图像测速技术所求解的速度场和DNS精确解之间在结构上是十分相似的，标量图像测速可以正确地提取速度场。

The theory and DNS testing of scalar image velocimetry

Scalar image velocimetry （SIV） is a new development turbulent measurement system for microstructure. In the high Schmidt number scalar turbulence, both of the time scale and the scalar dissipation length scale（ Batchelor scale） of pulsating scalar field are smaller than corresponding scales of pulsating velocity field： the time scale and the finest turbulence length scale（Kolmogorov scale）,the scalar filed shows more pulse intermittence than the velocity field. It means that the scalar field contains more information than the velocity field and the velocity field can be extracted from the scalar field of high Schmidt number. This paper detailedly introduce the theory of SIV, and under the guide of integral minimization algorithm the math formulation of integral minimization SIV is built according the scalar conservation transport equation and constraint conditions. Through variation three velocity component Euler characteristic equations of every point in the integral domain can be acquired, and by discretization of Euler characteristic equations one linear sparse equations set containing whole field information can be established. By solving the linear sparse equations set with variation iterative method, 3-dimensional velocity field of integral domain can be gained, and so the SIV image processing system is established. This paper also introduces the image acquisition method of 4D scalar field （3D space and 1 D time）, the image processing system is tested by DNS data of unit Schmdit number, and the result shows that the iterative computation result is same with DNS result and the integral minimization SIV can extract velocity field accurately.