Abstract Fanno theory provides an analytical model for one-dimensional confined viscous compressible flows. The model holds under the assumptions of adiabatic flow and constant cross-section channel. From theory, the differential of every flow-related quantity is expressed as a function of Mach number and friction factor. One-dimensional flow numerical models can be derived by discretizing Fanno equations. However, theory does not assess how to evaluate friction, while the model works properly only if friction is estimated correctly. Compressibility and turbulence act by deforming the velocity profile making it flatter. Assuming the friction factor function of the Reynolds number alone, in line with incompressible flow theory, is thus not correct. Better correlations should include the Mach number to address compressibility effects. Here, the impact of turbulence and compressibility on the velocity profiles in a micro-channel is analysed by means of CFD simulations. Friction factor correlations are deduced for turbulent micro-flows. The impact of the velocity profile on other quantities, such as dynamic pressure and bulk temperature, needed for the numerical model operation, is also evaluated. Additional correlations for these quantities overcome the instrinsic limits of the one-dimensional model, necessarily unaware of local velocity profiles, in a quasi-2D fashion significantly improving its predicting capabilities.

中文翻译：

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微通道中的可压缩范诺流：湍流的增强准二维数值模型

摘要 Fanno 理论为一维受限粘性可压缩流提供了一个分析模型。该模型在绝热流动和恒定截面通道的假设下成立。从理论上讲，每个流量相关量的微分都表示为马赫数和摩擦系数的函数。一维流动数值模型可以通过离散化范诺方程推导出来。然而，理论并没有评估如何评估摩擦，而模型只有在正确估计摩擦的情况下才能正常工作。可压缩性和湍流通过使速度剖面变形使其更平坦而起作用。因此，根据不可压缩流动理论，仅假设雷诺数的摩擦系数函数是不正确的。更好的相关性应该包括马赫数以解决可压缩性影响。这里，通过 CFD 模拟分析了湍流和可压缩性对微通道中速度分布的影响。推导出湍流微流的摩擦系数相关性。还评估了速度剖面对数值模型操作所需的其他量的影响，例如动态压力和整体温度。这些量的附加相关性克服了一维模型的内在限制，必然不知道局部速度剖面，以准二维方式显着提高其预测能力。还评估了数值模型操作所需的动态压力和整体温度等。这些量的附加相关性克服了一维模型的内在限制，必然不知道局部速度剖面，以准二维方式显着提高其预测能力。还评估了数值模型操作所需的动态压力和整体温度等。这些量的附加相关性克服了一维模型的内在限制，必然不知道局部速度剖面，以准二维方式显着提高其预测能力。