Abstract
Measured filtered density functions (FDFs) as well as assumed beta distribution model of mixture fraction and “subgrid” scale (SGS) scalar variance z′′2¯, used typically in large eddy simulations, were studied by analysing experimental data, obtained from two-dimensional planar, laser induced fluorescence measurements in isothermal swirling turbulent flows at a constant Reynolds number of 29 000 for different swirl numbers (0.3, 0.58, and 1.07). Two-dimensional spatial filtering, by using a box filter, was performed in order to obtain the filtered variables, namely, resolved mean and “subgrid” scale scalar variance. These were used as inputs for assumed beta distribution of mixture fraction and top-hat FDF shape estimates. The presumed beta distribution model, top-hat FDF, and the measured filtered density functions were used to integrate a laminar flamelet solution in order to calculate the corresponding resolved temperature. The experimentally measured FDFs varied with the flow swirl number and both axial and radial positions in the flow. The FDFs were unimodal at flow regions with low SGS scalar variance, z′′2¯< 0.01, and bimodal at regions with high SGS variance, z′′2¯> 0.02. Bimodal FDF could be observed for a filter size of approximately 1.5-2 times the Batchelor scale. Unimodal FDF could be observed for a filter size as large as four times the Batchelor scale under well-mixed conditions. In addition, two common computational models (a gradient assumption and a scale similarity model) for the SGS scalar variance were used with the aim to evaluate their validity through comparison with the experimental data. It was found that the gradient assumption model performed generally better than the scale similarity one.
Highlights
In Large Eddy Simulations (LESs) of turbulent reacting flows, spatially averaged versions of the equations describing fluid motion are usually solved on a grid, which is “coarse” relative to the smallest scales of fluid motion
We demonstrate that the filtered density functions (FDFs) can be bimodal even when the filter size is comparable to the Batchelor scale λβ
The FDFs were studied by analysing experimental data, obtained from two-dimensional planar, laser induced fluorescence scalar measurements in isothermal swirling turbulent flows
Summary
In Large Eddy Simulations (LESs) of turbulent reacting flows, spatially averaged versions of the equations describing fluid motion are usually solved on a grid, which is “coarse” relative to the smallest scales of fluid motion. In LES, the dynamics of scales that are larger than the filter width (the resolved scales) are captured explicitly, while the effects of the smallest or “subgrid” scales (SGSs) that are not resolved by the filter need to be modelled. The filtered quantity f (x,t) (velocity, mixture fraction, etc.) in physical space is defined as a convolution of the non-filtered field f (x′,t) with a function or convolution kernel, G∆ (x − x′) as follows:1 +∞. The low-pass spatial filter function G∆ G∆ (x − x′) dx = 1 and is independent of spatial has characteristic filter width location.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
