A multifractal model is developed to connect the Lagrangian multifractal dimensions with their Eulerian counterparts. We propose that the characteristic time scale of a Lagrangian quantity should be the Lagrangian time scale, and it should not be the Eulerian time scale which was widely used in previous studies on Lagrangian statistics. Using the present model, we can obtain the scaling exponents of Lagrangian velocity structure functions from the existing data or models of scaling exponents of Eulerian velocity structure functions. This model is validated by comparing its prediction with the results of experiments, direct numerical simulations, and the previous theoretical models. The comparison shows that the proposed model can better predict the scaling exponents of Lagrangian velocity structure functions, especially for orders larger than 6.
The Arrhenius law implies that reaction rate is a continuous function of temperature. However,the steady laminar flamelet model(SLFM) does not explicitly give this functional relationship. The present study addresses this relation in the SLFM.It is found that reaction rate is not continuous in the mixture-fraction space.As a result,the SLFM is unable to predict local extinction and reignition.Furthermore,we use the unstable branch of the'S-curve'to fill the gap between steady burning branch and extinction one,and find that this modification leads to a continuous dependent of reaction rate on temperature.Thus the modified SLFM can describe the local extinction and reignition.
Jian Zhang,~(a)) Guowei He,~(b)) and Guodong Jin LNM,Institute of Mechanics,Chinese Academy of Sciences,Beijing 100190,China
