Purpose

Cardiovascular engineering includes flows with fluid-dynamical stresses as a parameter of interest. Mechanical stresses are high-risk factors for blood damage and can be assessed by computational fluid dynamics. By now, it is not described how to calculate an adequate scalar stress out of turbulent flow regimes when the whole share of turbulence is not resolved by the simulation method and how this impacts the stress calculation.

Methods

We conducted direct numerical simulations (DNS) of test cases (a turbulent channel flow and the FDA nozzle) in order to access all scales of flow movement. After validation of both DNS with literature und experimental data using magnetic resonance imaging, the mechanical stress is calculated as a baseline. Afterwards, same flows are calculated using state-of-the-art turbulence models. The stresses are computed for every result using our definition of an equivalent scalar stress, which includes the influence from respective turbulence model, by using the parameter dissipation. Afterwards, the results are compared with the baseline data.

Results

The results show a good agreement regarding the computed stress. Even when no turbulence is resolved by the simulation method, the results agree well with DNS data. When the influence of non-resolved motion is neglected in the stress calculation, it is underpredicted in all cases.

Conclusion

With the used scalar stress formulation, it is possible to include information about the turbulence of the flow into the mechanical stress calculation even when the used simulation method does not resolve any turbulence.

中文翻译：

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考虑非分辨湍流尺度的等效标量应力公式

目的

心血管工程包括具有流体动力学应力的流动作为感兴趣的参数。机械应力是血液损伤的高风险因素，可以通过计算流体动力学进行评估。到目前为止，还没有描述当模拟方法无法解决整个湍流份额时如何从湍流流态中计算出足够的标量应力，以及这如何影响应力计算。

方法

我们对测试案例（湍流通道流和 FDA 喷嘴）进行了直接数值模拟 (DNS)，以访问所有尺度的流动运动。在使用文献和使用磁共振成像的实验数据验证 DNS 后，将机械应力计算为基线。之后，使用最先进的湍流模型计算相同的流动。使用我们对等效标量应力的定义（包括来自相应湍流模型的影响），通过使用参数耗散计算每个结果的应力。然后，将结果与基线数据进行比较。

结果

结果显示了计算应力的良好一致性。即使模拟方法没有解决湍流，结果与 DNS 数据也很吻合。当在应力计算中忽略非解析运动的影响时，在所有情况下都会被低估。

结论

使用所使用的标量应力公式，即使所使用的模拟方法无法解决任何湍流，也可以将有关流动湍流的信息包含到机械应力计算中。