Numerical simulation of turbulent flows in complex geometries using the CVS approach based on orthonormal wavelet decomposition

湍流反应流的特点是具有大范围的活动时间和空间尺度。在大多数情况下，不能实现小尺度与大尺度的解耦，慢尺度与快尺度的解耦。多尺度表示，如小波基，允许绕过这一障碍，因此，有希望建模和计算化学反应湍流。本项目的重点是应用新开发的相干涡模拟（CVS）方法来研究湍流反应流中的混合。在CVS方法中，守恒方程在小波滤波得到的压缩基中求解。大涡模拟（Large Eddy Simulation， LES）方法抛弃小尺度，模拟其对大尺度流动的影响，而CVS在流动演变过程中自动适应计算网格，以解决强梯度发展的区域。尽管CVS计算是在高度压缩的基础上执行的，因此节省了计算资源，但结果与从DNS计算中获得的结果非常一致，DNS计算不受模型限制，可以解析所有尺度。因此，这种新的计算方法特别适合于研究化学反应大多发生在精细尺度上且通常在空间中非常局部的反应流。本提案的目的是基于CVS开发新的多尺度湍流模型和数值代码，以精确模拟在化学工程和地球物理流动中许多应用中遇到的高雷诺数和高施密特数复杂几何形状的湍流反应流动。

Turbulent reacting flows are characterized by their large range of active temporal and spatial scales. In most cases a decoupling of the small from the large spatial scales and the slow from the fast temporal scales cannot be achieved. Multiscale representations, such as wavelet bases, allow to circumvent this obstruction and are, therefore, promising for modelling and computing chemically reacting turbulent flows. The project is focused on the application of the newly developed Coherent Vortex Simulation (CVS) method to study the mixing in turbulent reacting flows. In the CVS method the conservation equations are solved in a compressed basis obtained by wavelet filtering. Compared to the state of the art in modelling, Large Eddy Simulation (LES) methods which discard the small scales and model its influence on the large scales of the flow, CVS automatically adapts the computational grid during the flow evolution to resolve the regions where strong gradients develop. Even though CVS calculations are performed in a highly compressed basis and, therefore, save computational resources, the results are very consistent with those obtained from DNS calculations, which are model free and resolve all scales. Thus, this new computational method is particularly well suited to study reacting flows where the chemical reactions mostly occur on fine scales and often very locally in space. The aim of this proposal is to develop new multiscale turbulence models and numerical codes based on CVS to accurately simulate turbulent reacting flows in complex geometries at high Reynolds numbers and high Schmidt numbers, as encountered in many applications in chemical engineering and in geophysical flows.