Partially Averaged Navier–Stokes computations can employ three different approaches for specifying the ratio of modelled-to-total turbulence kinetic energy fk. Use can be made of either a constant, a spatially- or a spatially- and temporally-varying value. This work compares different estimates for fk found in literature and evaluates them for two test-cases: a circular cylinder at Re=3900 and a turbulent channel flow at Reτ=395. Additionally, the estimates are compared to the a posteriori computed ratio of modelled-to-total turbulence kinetic energy()hfk˜ obtained from the PANS flow solution. The trends observed for the estimates are similar, although the magnitude varies significantly. All spatially varying fk approaches reduce the PANS model to a DES-like model, thereby entangling modelling and discretisation errors. At the same time, fk˜ shows that the behaviour of these estimates is incorrect: fk becomes too large near the wall of the object and in the far field. It is observed that fk˜ is always lower than the set value, when using fk fixed in space and time. Finally, it is clear that the estimates, applied to internal, boundary layer, flows yield too high values for fk. In order to minimise errors and increase the reliability of industrial CFD results, the approach with a constant fk is still preferable, assuming suitably fine grids are used.

中文翻译：

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关于部分平均 Navier-Stokes 分辨率估计的准确性

部分平均 Navier-Stokes 计算可以采用三种不同的方法来指定建模与总湍流动能 fk 的比率。可以使用常数、空间或空间和时间变化的值。这项工作比较了文献中对 fk 的不同估计，并针对两个测试案例对它们进行了评估：Re=3900 的圆柱体和 Reτ=395 的湍流通道流。此外，将估计值与从 PANS 流动解获得的模型化总湍流动能 ()hfk 的后验计算比率进行比较。观察到的估计趋势是相似的，尽管幅度差异很大。所有空间变化的 fk 方法都将 PANS 模型简化为类似 DES 的模型，从而纠缠建模和离散化错误。同时，fk~表明这些估计的行为是不正确的：fk 在物体壁附近和远场中变得太大。可以看出，当使用空间和时间固定的 fk 时，fk~总是低于设定值。最后，很明显，应用于内部边界层的估计流量产生了过高的 fk 值。为了最大限度地减少误差并提高工业 CFD 结果的可靠性，假设使用了合适的精细网格，使用恒定 fk 的方法仍然是优选的。