From Direct Numerical Simulations to Data-Driven Models: Insights into Mean Velocity Profiles and Turbulent Stresses in Channel Flows
In this paper, we compare three mathematical models for the mean velocity and Reynolds stress profiles for fully developed pressure-driven turbulent channel flow with the aim of assessing the level of accuracy of each model. Each model is valid over the whole boundary layer thickness (0 <inline-f...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-02-01
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| Series: | Modelling |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2673-3951/6/1/18 |
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| Summary: | In this paper, we compare three mathematical models for the mean velocity and Reynolds stress profiles for fully developed pressure-driven turbulent channel flow with the aim of assessing the level of accuracy of each model. Each model is valid over the whole boundary layer thickness (0 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>≤</mo><mi>y</mi><mo>≤</mo></mrow></semantics></math></inline-formula> <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>δ</mi></mrow></semantics></math></inline-formula>), and it is formulated in terms of a law of the wall and a law of the wake. To calibrate the mathematical models, we use data obtained by direct numerical simulations (DNS) of pressure-driven turbulent channel flow in the range 182 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>≤</mo><msub><mrow><mi>R</mi><mi>e</mi></mrow><mrow><mi>τ</mi></mrow></msub><mo>≤</mo><mo> </mo></mrow></semantics></math></inline-formula>10,049. The models selected for performance evaluation are two models (Musker’s and AL84) originally developed based on high Reynolds boundary layer experimental data and Luchini’s model, which was developed when some DNS data were also available for wall-bounded turbulent flows. Differences are quantified in terms of local relative or absolute errors. Luchini’s model outperforms the other two models in the “low” and “intermediate” Reynolds number cases (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>R</mi><mi>e</mi></mrow><mrow><mi>τ</mi></mrow></msub><mo>=</mo></mrow></semantics></math></inline-formula> 182 to 5186). However, for the “high” Reynolds number cases (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>R</mi><mi>e</mi></mrow><mrow><mi>τ</mi></mrow></msub><mo>=</mo></mrow></semantics></math></inline-formula> 8016 and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>R</mi><mi>e</mi></mrow><mrow><mi>τ</mi></mrow></msub><mo>=</mo></mrow></semantics></math></inline-formula> 10,049). Luchini’s model exhibits larger errors than the other two models. Both Musker’s and AL84 models exhibit comparable accuracy levels when compared with the DNS datasets, and their performance improves as the Reynolds number increases. |
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| ISSN: | 2673-3951 |